<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>CPCTC: Corresponding Parts</title>
  <style>
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      max-width: 540px;
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      font-size: 11px;
      font-weight: 700;
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      letter-spacing: 0.04em;
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      font-size: 13px;
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      height: 9px;
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</head>
<body>

  
  <header class="header">
    <div class="title">Corresponding Parts of Congruent Triangles (CPCTC)</div>
    <div class="badge-bar">
      <span class="badge-main">△ABC ≅ △DEF</span>
      <span class="map-badge">(A↔D, B↔E, C↔F)</span>
    </div>
  </header>

  
  <div class="svg-container">
    <svg viewBox="0 0 460 210" aria-label="Congruent Triangles ABC and DEF">
      <defs>
        
      </defs>

      
      <g opacity="0.35" stroke="#94a3b8" stroke-dasharray="3 3" stroke-width="1.2">
        <line x1="75" y1="35" x2="305" y2="35" />
        <line x1="30" y1="175" x2="260" y2="175" />
        <line x1="185" y1="165" x2="415" y2="165" />
      </g>

      
      
      <polygon points="75,35 30,175 185,165" class="tri-fill tri-outline" />

      
      
      <g class="geom-part c-cyan" data-key="angA" stroke="#0284c7" stroke-width="2.2" fill="none">
        <path d="M 68,56 A 25 25 0 0 0 88,50" />
      </g>
      
      <g class="geom-part c-purple" data-key="angB" stroke="#9333ea" stroke-width="2.2" fill="none">
        <path d="M 39,147 A 30 30 0 0 1 59,173" />
        <path d="M 46,143 A 36 36 0 0 1 66,172" />
      </g>
      
      <g class="geom-part c-pink" data-key="angC" stroke="#db2777" stroke-width="2.2" fill="none">
        <path d="M 158,166 A 28 28 0 0 1 170,147" />
        <path d="M 152,166 A 34 34 0 0 1 166,143" />
        <path d="M 146,167 A 40 40 0 0 1 162,139" />
      </g>

      
      
      <g class="geom-part c-blue" data-key="side1">
        <line x1="75" y1="35" x2="30" y2="175" stroke="#2563eb" stroke-width="3" stroke-linecap="round" />
        <line x1="46" y1="102" x2="58" y2="107" stroke="#2563eb" stroke-width="2.5" stroke-linecap="round" />
      </g>
      
      <g class="geom-part c-green" data-key="side2">
        <line x1="30" y1="175" x2="185" y2="165" stroke="#16a34a" stroke-width="3" stroke-linecap="round" />
        <line x1="104" y1="165" x2="102" y2="177" stroke="#16a34a" stroke-width="2.5" stroke-linecap="round" />
        <line x1="110" y1="165" x2="108" y2="177" stroke="#16a34a" stroke-width="2.5" stroke-linecap="round" />
      </g>
      
      <g class="geom-part c-orange" data-key="side3">
        <line x1="75" y1="35" x2="185" y2="165" stroke="#ea580c" stroke-width="3" stroke-linecap="round" />
        <line x1="123" y1="104" x2="135" y2="94" stroke="#ea580c" stroke-width="2.5" stroke-linecap="round" />
        <line x1="128" y1="109" x2="140" y2="99" stroke="#ea580c" stroke-width="2.5" stroke-linecap="round" />
        <line x1="133" y1="114" x2="145" y2="104" stroke="#ea580c" stroke-width="2.5" stroke-linecap="round" />
      </g>

      
      <text x="75" y="18" class="v-label">A</text>
      <text x="14" y="184" class="v-label">B</text>
      <text x="201" y="174" class="v-label">C</text>


      
      
      <polygon points="305,35 260,175 415,165" class="tri-fill tri-outline" />

      
      
      <g class="geom-part c-cyan" data-key="angA" stroke="#0284c7" stroke-width="2.2" fill="none">
        <path d="M 298,56 A 25 25 0 0 0 318,50" />
      </g>
      
      <g class="geom-part c-purple" data-key="angB" stroke="#9333ea" stroke-width="2.2" fill="none">
        <path d="M 269,147 A 30 30 0 0 1 289,173" />
        <path d="M 276,143 A 36 36 0 0 1 296,172" />
      </g>
      
      <g class="geom-part c-pink" data-key="angC" stroke="#db2777" stroke-width="2.2" fill="none">
        <path d="M 388,166 A 28 28 0 0 1 400,147" />
        <path d="M 382,166 A 34 34 0 0 1 396,143" />
        <path d="M 376,167 A 40 40 0 0 1 392,139" />
      </g>

      
      
      <g class="geom-part c-blue" data-key="side1">
        <line x1="305" y1="35" x2="260" y2="175" stroke="#2563eb" stroke-width="3" stroke-linecap="round" />
        <line x1="276" y1="102" x2="288" y2="107" stroke="#2563eb" stroke-width="2.5" stroke-linecap="round" />
      </g>
      
      <g class="geom-part c-green" data-key="side2">
        <line x1="260" y1="175" x2="415" y2="165" stroke="#16a34a" stroke-width="3" stroke-linecap="round" />
        <line x1="334" y1="165" x2="332" y2="177" stroke="#16a34a" stroke-width="2.5" stroke-linecap="round" />
        <line x1="340" y1="165" x2="338" y2="177" stroke="#16a34a" stroke-width="2.5" stroke-linecap="round" />
      </g>
      
      <g class="geom-part c-orange" data-key="side3">
        <line x1="305" y1="35" x2="415" y2="165" stroke="#ea580c" stroke-width="3" stroke-linecap="round" />
        <line x1="353" y1="104" x2="365" y2="94" stroke="#ea580c" stroke-width="2.5" stroke-linecap="round" />
        <line x1="358" y1="109" x2="370" y2="99" stroke="#ea580c" stroke-width="2.5" stroke-linecap="round" />
        <line x1="363" y1="114" x2="375" y2="104" stroke="#ea580c" stroke-width="2.5" stroke-linecap="round" />
      </g>

      
      <text x="305" y="18" class="v-label">D</text>
      <text x="244" y="184" class="v-label">E</text>
      <text x="431" y="174" class="v-label">F</text>
    </svg>
  </div>

  
  <div class="matrix-section">
    <div class="columns-wrap">
      
      <div class="matrix-col">
        <div class="col-header">Congruent Sides</div>
        <button class="pill-btn c-blue" data-target="side1">
          <div class="pill-content">
            <span class="pill-tag bg-blue"></span>
            <span>AB ≅ DE</span>
          </div>
          <span>1 tick</span>
        </button>
        <button class="pill-btn c-green" data-target="side2">
          <div class="pill-content">
            <span class="pill-tag bg-green"></span>
            <span>BC ≅ EF</span>
          </div>
          <span>2 ticks</span>
        </button>
        <button class="pill-btn c-orange" data-target="side3">
          <div class="pill-content">
            <span class="pill-tag bg-orange"></span>
            <span>AC ≅ DF</span>
          </div>
          <span>3 ticks</span>
        </button>
      </div>

      
      <div class="matrix-col">
        <div class="col-header">Congruent Angles</div>
        <button class="pill-btn c-cyan" data-target="angA">
          <div class="pill-content">
            <span class="pill-tag bg-cyan"></span>
            <span>∠A ≅ ∠D</span>
          </div>
          <span>1 arc</span>
        </button>
        <button class="pill-btn c-purple" data-target="angB">
          <div class="pill-content">
            <span class="pill-tag bg-purple"></span>
            <span>∠B ≅ ∠E</span>
          </div>
          <span>2 arcs</span>
        </button>
        <button class="pill-btn c-pink" data-target="angC">
          <div class="pill-content">
            <span class="pill-tag bg-pink"></span>
            <span>∠C ≅ ∠F</span>
          </div>
          <span>3 arcs</span>
        </button>
      </div>
    </div>

    
    <button class="reset-btn" id="resetBtn">Show All Correspondences</button>
  </div>

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      // Update Pill buttons state
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</body>
</html>

Understanding Geometric Congruence and CPCTC

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>CPCTC Worked Example</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
    }

    body {
      background: #ffffff;
      color: #1e293b;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
    }

    .app-container {
      width: 100%;
      max-width: 540px;
      display: flex;
      flex-direction: column;
      gap: 10px;
    }

    /* Congruence statement bar */
    .statement-box {
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 8px 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 4px;
    }

    .statement-row {
      display: flex;
      align-items: center;
      gap: 12px;
      font-size: 20px;
      font-weight: 700;
      letter-spacing: 0.5px;
    }

    .tri-letters {
      display: inline-flex;
      gap: 2px;
    }

    .letter {
      display: inline-flex;
      align-items: center;
      justify-content: center;
      width: 24px;
      height: 28px;
      border-radius: 6px;
      transition: background-color 0.25s, color 0.25s, box-shadow 0.25s;
    }

    .pos-tags {
      display: flex;
      justify-content: space-between;
      width: 76px;
      font-size: 10px;
      font-weight: 600;
      color: #94a3b8;
      padding: 0 4px;
    }

    /* Color highlights for correspondence */
    .hl-blue {
      background: #dbeafe;
      color: #1d4ed8;
      box-shadow: inset 0 0 0 1.5px #3b82f6;
    }

    .hl-green {
      background: #d1fae5;
      color: #047857;
      box-shadow: inset 0 0 0 1.5px #10b981;
    }

    /* Visual Triangles Area */
    .triangles-view {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 8px;
      width: 100%;
    }

    .tri-card {
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 10px;
      padding: 6px;
      display: flex;
      flex-direction: column;
      align-items: center;
      position: relative;
    }

    .tri-svg {
      width: 100%;
      height: 110px;
      overflow: visible;
    }

    /* Side label styling in SVG */
    .side-label {
      font-size: 12px;
      font-weight: 700;
      fill: #475569;
    }

    .side-label.blue-active {
      fill: #1d4ed8;
      font-weight: 800;
    }

    .side-label.green-active {
      fill: #047857;
      font-weight: 800;
    }

    .tri-edge {
      stroke: #cbd5e1;
      stroke-width: 2.5;
      stroke-linecap: round;
      transition: stroke 0.25s, stroke-width 0.25s;
    }

    .tri-edge.blue-active {
      stroke: #2563eb;
      stroke-width: 4;
    }

    .tri-edge.green-active {
      stroke: #059669;
      stroke-width: 4;
    }

    /* Math Step Box */
    .step-display {
      background: #ffffff;
      border: 1px solid #cbd5e1;
      border-radius: 12px;
      padding: 10px 14px;
      min-height: 94px;
      display: flex;
      flex-direction: column;
      justify-content: center;
      align-items: center;
      text-align: center;
      gap: 6px;
      box-shadow: 0 1px 3px rgba(0,0,0,0.04);
    }

    .step-badge {
      display: inline-flex;
      align-items: center;
      gap: 6px;
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      padding: 2px 8px;
      border-radius: 999px;
      background: #eff6ff;
      color: #1d4ed8;
    }

    .math-main {
      font-size: 18px;
      font-weight: 700;
      color: #0f172a;
      display: flex;
      align-items: center;
      gap: 8px;
      flex-wrap: wrap;
      justify-content: center;
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    .math-sub {
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
    }

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    .controls {
      display: flex;
      align-items: center;
      justify-content: space-between;
      gap: 8px;
      width: 100%;
      padding-top: 2px;
    }

    .step-pills {
      display: flex;
      gap: 6px;
      align-items: center;
    }

    .pill-btn {
      border: 1px solid #cbd5e1;
      background: #f8fafc;
      color: #475569;
      font-size: 12px;
      font-weight: 700;
      padding: 6px 12px;
      border-radius: 8px;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      gap: 4px;
      transition: background 0.15s, color 0.15s, border-color 0.15s;
    }

    .pill-btn.active {
      background: #2563eb;
      color: #ffffff;
      border-color: #2563eb;
    }

    .nav-btn {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      color: #1e293b;
      font-size: 13px;
      font-weight: 600;
      padding: 6px 12px;
      border-radius: 8px;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      justify-content: center;
      transition: background 0.15s;
    }

    .nav-btn:hover {
      background: #e2e8f0;
    }

    @media (max-width: 400px) {
      .pill-btn {
        padding: 6px 8px;
        font-size: 11px;
      }
      .statement-row {
        font-size: 17px;
      }
      .math-main {
        font-size: 16px;
      }
    }
  </style>
</head>
<body>

<div class="app-container">
  
  <div class="statement-box">
    <div class="statement-row">
      <div style="display:flex; flex-direction:column; align-items:center;">
        <div class="tri-letters">
          <span>△</span>
          <span id="let-p" class="letter">P</span>
          <span id="let-q" class="letter">Q</span>
          <span id="let-r" class="letter">R</span>
        </div>
        <div class="pos-tags">
          <span>1st</span><span>2nd</span><span>3rd</span>
        </div>
      </div>

      <span style="color:#64748b; font-weight:800; font-size:18px;">≅</span>

      <div style="display:flex; flex-direction:column; align-items:center;">
        <div class="tri-letters">
          <span>△</span>
          <span id="let-s" class="letter">S</span>
          <span id="let-t" class="letter">T</span>
          <span id="let-u" class="letter">U</span>
        </div>
        <div class="pos-tags">
          <span>1st</span><span>2nd</span><span>3rd</span>
        </div>
      </div>
    </div>
  </div>

  
  <div class="triangles-view">
    
    <div class="tri-card">
      <svg class="tri-svg" viewBox="0 0 160 110">
        
        <line id="edge-pr" class="tri-edge" x1="25" y1="90" x2="135" y2="90" />
        <line id="edge-qr" class="tri-edge" x1="25" y1="20" x2="135" y2="90" />
        <line id="edge-pq" class="tri-edge" x1="25" y1="90" x2="25" y2="20" />

        
        <circle cx="25" cy="90" r="3.5" fill="#1e293b" />
        <circle cx="25" cy="20" r="3.5" fill="#1e293b" />
        <circle cx="135" cy="90" r="3.5" fill="#1e293b" />

        <text x="12" y="96" font-size="12" font-weight="700" fill="#1e293b">P</text>
        <text x="12" y="20" font-size="12" font-weight="700" fill="#1e293b">Q</text>
        <text x="142" y="96" font-size="12" font-weight="700" fill="#1e293b">R</text>

        
        <text id="lbl-pq" class="side-label" x="32" y="58" text-anchor="start">2x + 5</text>
        <text id="lbl-pr" class="side-label" x="80" y="105" text-anchor="middle">PR = ?</text>
      </svg>
    </div>

    
    <div class="tri-card">
      <svg class="tri-svg" viewBox="0 0 160 110">
        
        <line id="edge-su" class="tri-edge" x1="25" y1="90" x2="135" y2="90" />
        <line id="edge-tu" class="tri-edge" x1="25" y1="20" x2="135" y2="90" />
        <line id="edge-st" class="tri-edge" x1="25" y1="90" x2="25" y2="20" />

        
        <circle cx="25" cy="90" r="3.5" fill="#1e293b" />
        <circle cx="25" cy="20" r="3.5" fill="#1e293b" />
        <circle cx="135" cy="90" r="3.5" fill="#1e293b" />

        <text x="12" y="96" font-size="12" font-weight="700" fill="#1e293b">S</text>
        <text x="12" y="20" font-size="12" font-weight="700" fill="#1e293b">T</text>
        <text x="142" y="96" font-size="12" font-weight="700" fill="#1e293b">U</text>

        
        <text id="lbl-st" class="side-label" x="32" y="58" text-anchor="start">19</text>
        <text id="lbl-su" class="side-label" x="80" y="105" text-anchor="middle">14</text>
      </svg>
    </div>
  </div>

  
  <div class="step-display">
    <div id="step-badge" class="step-badge">Step 1 of 4</div>
    <div id="step-math" class="math-main">PQ corresponds to ST</div>
    <div id="step-desc" class="math-sub">Letters 1–2 match letters 1–2</div>
  </div>

  
  <div class="controls">
    <button class="nav-btn" onclick="prevStep()">◀</button>
    <div class="step-pills">
      <button class="pill-btn active" onclick="goToStep(0)">1: Match</button>
      <button class="pill-btn" onclick="goToStep(1)">2: Setup</button>
      <button class="pill-btn" onclick="goToStep(2)">3: Solve</button>
      <button class="pill-btn" onclick="goToStep(3)">4: PR</button>
    </div>
    <button id="play-btn" class="nav-btn" onclick="togglePlay()">⏸</button>
    <button class="nav-btn" onclick="nextStep()">▶</button>
  </div>
</div>

<script>
  let currentStep = 0;
  let isPlaying = true;
  let timer = null;

  const stepsData = [
    {
      badge: "Step 1: Corresponding Sides",
      math: '<span style="color:#2563eb;">PQ</span> = <span style="color:#2563eb;">ST</span> &nbsp;|&nbsp; <span style="color:#059669;">PR</span> = <span style="color:#059669;">SU</span>',
      sub: "1st-2nd letters & 1st-3rd letters correspond",
      hlBlue: ['let-p', 'let-q', 'let-s', 'let-t'],
      hlGreen: ['let-r', 'let-u'],
      edgeBlue: ['edge-pq', 'edge-st'],
      edgeGreen: ['edge-pr', 'edge-su'],
      lblBlue: ['lbl-pq', 'lbl-st'],
      lblGreen: ['lbl-su'],
      prText: "PR = ?"
    },
    {
      badge: "Step 2: Set Up Equation",
      math: '2x + 5 = 19',
      sub: "Substitute side lengths: PQ = ST",
      hlBlue: ['let-p', 'let-q', 'let-s', 'let-t'],
      hlGreen: [],
      edgeBlue: ['edge-pq', 'edge-st'],
      edgeGreen: [],
      lblBlue: ['lbl-pq', 'lbl-st'],
      lblGreen: [],
      prText: "PR = ?"
    },
    {
      badge: "Step 3: Solve for x",
      math: '2x = 14 &nbsp;➔&nbsp; <span style="color:#2563eb;">x = 7</span>',
      sub: "Subtract 5, then divide by 2",
      hlBlue: ['let-p', 'let-q', 'let-s', 'let-t'],
      hlGreen: [],
      edgeBlue: ['edge-pq', 'edge-st'],
      edgeGreen: [],
      lblBlue: ['lbl-pq', 'lbl-st'],
      lblGreen: [],
      prText: "PR = ?"
    },
    {
      badge: "Step 4: Find PR using CPCTC",
      math: 'PR = SU &nbsp;➔&nbsp; <span style="color:#059669;">PR = 14</span>',
      sub: "Corresponding side length is exact duplicate",
      hlBlue: [],
      hlGreen: ['let-p', 'let-r', 'let-s', 'let-u'],
      edgeBlue: [],
      edgeGreen: ['edge-pr', 'edge-su'],
      lblBlue: [],
      lblGreen: ['lbl-pr', 'lbl-su'],
      prText: "PR = 14"
    }
  ];

  function renderStep(idx) {
    const data = stepsData[idx];

    // Update text
    document.getElementById('step-badge').textContent = data.badge;
    document.getElementById('step-math').innerHTML = data.math;
    document.getElementById('step-desc').textContent = data.sub;
    document.getElementById('lbl-pr').textContent = data.prText;

    // Reset all highlights
    const allLetters = ['let-p', 'let-q', 'let-r', 'let-s', 'let-t', 'let-u'];
    allLetters.forEach(id => {
      const el = document.getElementById(id);
      el.className = 'letter';
    });

    const allEdges = ['edge-pq', 'edge-pr', 'edge-qr', 'edge-st', 'edge-su', 'edge-tu'];
    allEdges.forEach(id => {
      const el = document.getElementById(id);
      el.classList.remove('blue-active', 'green-active');
    });

    const allLabels = ['lbl-pq', 'lbl-pr', 'lbl-st', 'lbl-su'];
    allLabels.forEach(id => {
      const el = document.getElementById(id);
      el.classList.remove('blue-active', 'green-active');
    });

    // Apply Blue Highlights
    data.hlBlue.forEach(id => document.getElementById(id).classList.add('hl-blue'));
    data.edgeBlue.forEach(id => document.getElementById(id).classList.add('blue-active'));
    data.lblBlue.forEach(id => document.getElementById(id).classList.add('blue-active'));

    // Apply Green Highlights
    data.hlGreen.forEach(id => document.getElementById(id).classList.add('hl-green'));
    data.edgeGreen.forEach(id => document.getElementById(id).classList.add('green-active'));
    data.lblGreen.forEach(id => document.getElementById(id).classList.add('green-active'));

    // Update buttons
    const pills = document.querySelectorAll('.pill-btn');
    pills.forEach((p, i) => {
      if (i === idx) p.classList.add('active');
      else p.classList.remove('active');
    });
  }

  function goToStep(idx) {
    currentStep = idx;
    renderStep(currentStep);
    resetTimer();
  }

  function nextStep() {
    currentStep = (currentStep + 1) % stepsData.length;
    renderStep(currentStep);
    resetTimer();
  }

  function prevStep() {
    currentStep = (currentStep - 1 + stepsData.length) % stepsData.length;
    renderStep(currentStep);
    resetTimer();
  }

  function togglePlay() {
    isPlaying = !isPlaying;
    document.getElementById('play-btn').textContent = isPlaying ? '⏸' : '▶';
    if (isPlaying) {
      startTimer();
    } else {
      clearInterval(timer);
    }
  }

  function startTimer() {
    clearInterval(timer);
    timer = setInterval(() => {
      currentStep = (currentStep + 1) % stepsData.length;
      renderStep(currentStep);
    }, 4000);
  }

  function resetTimer() {
    if (isPlaying) {
      startTimer();
    }
  }

  // Initial render
  renderStep(0);
  startTimer();
</script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      width: 100%;
      background: #f8f9fa;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      padding: 10px 8px;
      user-select: none;
    }

    .header-info {
      text-align: center;
      margin-bottom: 6px;
    }

    .step-desc {
      font-size: 13px;
      font-weight: 600;
      color: #4f46e5;
      min-height: 18px;
      transition: color 0.2s ease;
    }

    .controls {
      display: flex;
      flex-wrap: wrap;
      gap: 5px;
      justify-content: center;
      align-items: center;
      width: 100%;
      max-width: 520px;
      margin-bottom: 8px;
    }

    .btn {
      appearance: none;
      border: 1px solid #cbd5e1;
      background: #ffffff;
      color: #1e2945;
      padding: 5px 10px;
      border-radius: 18px;
      font-size: 12px;
      font-weight: 600;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      justify-content: center;
      gap: 4px;
      transition: background-color 0.15s, color 0.15s, border-color 0.15s, box-shadow 0.15s;
    }

    .btn:hover {
      border-color: #94a3b8;
      background: #f1f5f9;
    }

    .btn.active {
      background: #4f46e5;
      border-color: #4f46e5;
      color: #ffffff;
      box-shadow: 0 2px 6px rgba(79, 70, 229, 0.3);
    }

    .btn-play {
      width: 28px;
      height: 28px;
      padding: 0;
      border-radius: 50%;
      font-size: 11px;
    }

    @media (max-width: 400px) {
      .btn {
        padding: 4px 7px;
        font-size: 11px;
      }
      .btn-play {
        width: 26px;
        height: 26px;
      }
      .step-desc {
        font-size: 12px;
      }
    }

    .diagram-area {
      width: 100%;
      max-width: 520px;
      position: relative;
    }

    svg {
      width: 100%;
      height: auto;
      display: block;
      overflow: visible;
    }

    .congruence-badge {
      position: absolute;
      bottom: 6px;
      left: 50%;
      transform: translateX(-50%) translateY(6px);
      background: #4f46e5;
      color: #ffffff;
      font-size: 14px;
      font-weight: 700;
      padding: 5px 16px;
      border-radius: 20px;
      box-shadow: 0 3px 10px rgba(79, 70, 229, 0.35);
      opacity: 0;
      pointer-events: none;
      transition: opacity 0.3s ease, transform 0.3s ease;
      letter-spacing: 0.5px;
      white-space: nowrap;
    }

    .congruence-badge.visible {
      opacity: 1;
      transform: translateX(-50%) translateY(0);
    }

    .v-label {
      font-size: 14px;
      font-weight: 700;
      fill: #1e2945;
      text-anchor: middle;
      dominant-baseline: central;
    }

    .s-label {
      font-size: 12px;
      font-weight: 600;
      fill: #64748b;
      text-anchor: middle;
      dominant-baseline: central;
    }

    .lbl-blue {
      fill: #4f46e5;
      font-weight: 700;
    }

    .ghost-line {
      stroke: #cbd5e1;
      stroke-dasharray: 4,4;
      stroke-width: 1.5;
    }
  </style>
</head>
<body>

  <div class="header-info">
    <div class="step-desc" id="stepDesc">Initial position of △ABC and target △DEF</div>
  </div>

  <div class="controls">
    <button class="btn btn-play" id="playBtn" title="Play / Pause">⏸</button>
    <button class="btn active" data-step="0">Start</button>
    <button class="btn" data-step="1">1. Translate</button>
    <button class="btn" data-step="2">2. Rotate</button>
    <button class="btn" data-step="3">3. Reflect</button>
  </div>

  <div class="diagram-area">
    <svg viewBox="0 0 520 235">
      <defs>
        
        <filter id="glow" x="-30%" y="-30%" width="160%" height="160%">
          <feGaussianBlur stdDeviation="3" result="blur" />
          <feComposite in="SourceGraphic" in2="blur" operator="over" />
        </filter>
      </defs>

      
      <g id="targetGroup">
        <polygon points="440,70 440,190 350,190" fill="#f1f5f9" stroke="#94a3b8" stroke-width="2" stroke-dasharray="5,4" stroke-linejoin="round"/>
        
        <path d="M 426 190 L 426 176 L 440 176" fill="none" stroke="#94a3b8" stroke-width="1.5" />
        
        <text class="s-label" x="456" y="130">4</text>
        <text class="s-label" x="395" y="206">3</text>
        <text class="s-label" x="382" y="120">5</text>
        
        <text class="v-label" x="440" y="52">D</text>
        <text class="v-label" x="456" y="196">E</text>
        <text class="v-label" x="334" y="196">F</text>
      </g>

      
      <line id="reflAxis" x1="395" y1="35" x2="395" y2="215" stroke="#a5b4fc" stroke-width="1.5" stroke-dasharray="4,4" opacity="0"/>
      <text id="reflLabel" x="395" y="26" font-size="11" font-weight="600" fill="#6366f1" text-anchor: middle text-anchor="middle" opacity="0">Line of Reflection</text>

      
      <g id="movingGroup">
        
        <polygon id="glowPoly" points="160,190 160,100 40,190" fill="none" stroke="#4f46e5" stroke-width="6" stroke-linejoin="round" opacity="0" filter="url(#glow)"/>
        
        <polygon id="polyABC" points="160,190 160,100 40,190" fill="rgba(79, 70, 229, 0.18)" stroke="#4f46e5" stroke-width="2.5" stroke-linejoin="round"/>
        
        <path id="rightAngleMark" d="M 160 176 L 146 176 L 146 190" fill="none" stroke="#4f46e5" stroke-width="1.5" />

        
        <circle id="dotA" cx="160" cy="190" r="4.5" fill="#4f46e5" stroke="#ffffff" stroke-width="1.5"/>
        <circle id="dotB" cx="160" cy="100" r="4.5" fill="#4f46e5" stroke="#ffffff" stroke-width="1.5"/>
        <circle id="dotC" cx="40" cy="190" r="4.5" fill="#4f46e5" stroke="#ffffff" stroke-width="1.5"/>

        
        <text id="lblAB" class="s-label lbl-blue" x="176" y="145">3</text>
        <text id="lblAC" class="s-label lbl-blue" x="100" y="206">4</text>
        <text id="lblBC" class="s-label lbl-blue" x="90" y="135">5</text>

        
        <text id="txtA" class="v-label" x="176" y="200">A</text>
        <text id="txtB" class="v-label" x="160" y="82">B</text>
        <text id="txtC" class="v-label" x="25" y="195">C</text>
      </g>
    </svg>

    <div class="congruence-badge" id="badge">△ABC ≅ △DEF</div>
  </div>

  <script>
    // Exact geometric states mapping ABC onto DEF
    // Leg AB = 3 (90px), Leg AC = 4 (120px), Hypotenuse BC = 5 (150px)
    const states = [
      // 0: Start
      {
        desc: "Initial position of △ABC and target △DEF",
        A: { x: 160, y: 190 },
        B: { x: 160, y: 100 },
        C: { x: 40, y: 190 },
        lblAB: { x: 176, y: 145 },
        lblAC: { x: 100, y: 206 },
        lblBC: { x: 90, y: 135 },
        txtA: { x: 176, y: 200 },
        txtB: { x: 160, y: 82 },
        txtC: { x: 25, y: 195 },
        refl: 0
      },
      // 1: Translate (slide right +90px)
      {
        desc: "1. Translation: slide △ABC horizontally by +90 px",
        A: { x: 250, y: 190 },
        B: { x: 250, y: 100 },
        C: { x: 130, y: 190 },
        lblAB: { x: 266, y: 145 },
        lblAC: { x: 190, y: 206 },
        lblBC: { x: 180, y: 135 },
        txtA: { x: 266, y: 200 },
        txtB: { x: 250, y: 82 },
        txtC: { x: 115, y: 195 },
        refl: 0
      },
      // 2: Rotate 90° clockwise around A(250, 190)
      {
        desc: "2. Rotation: turn △ABC 90° clockwise about vertex A",
        A: { x: 250, y: 190 },
        B: { x: 340, y: 190 },
        C: { x: 250, y: 70 },
        lblAB: { x: 295, y: 206 },
        lblAC: { x: 234, y: 130 },
        lblBC: { x: 305, y: 120 },
        txtA: { x: 235, y: 200 },
        txtB: { x: 355, y: 195 },
        txtC: { x: 250, y: 52 },
        refl: 0.8
      },
      // 3: Reflect across line x = 395 onto DEF
      {
        desc: "3. Reflection: flip △ABC across the line to overlap △DEF",
        A: { x: 440, y: 190 }, // maps to E
        B: { x: 350, y: 190 }, // maps to F
        C: { x: 440, y: 70 },  // maps to D
        lblAB: { x: 395, y: 206 },
        lblAC: { x: 456, y: 130 },
        lblBC: { x: 382, y: 120 },
        txtA: { x: 456, y: 196 },
        txtB: { x: 334, y: 196 },
        txtC: { x: 440, y: 52 },
        refl: 0
      }
    ];

    let current = 0;
    let playing = true;
    let autoTimer = null;
    let animFrame = null;

    // Current animated coordinates
    const cur = JSON.parse(JSON.stringify(states[0]));
    let curRefl = 0;
    let glowOpacity = 0;

    const polyABC = document.getElementById('polyABC');
    const glowPoly = document.getElementById('glowPoly');
    const rightAngleMark = document.getElementById('rightAngleMark');
    const dotA = document.getElementById('dotA');
    const dotB = document.getElementById('dotB');
    const dotC = document.getElementById('dotC');
    const txtA = document.getElementById('txtA');
    const txtB = document.getElementById('txtB');
    const txtC = document.getElementById('txtC');
    const lblAB = document.getElementById('lblAB');
    const lblAC = document.getElementById('lblAC');
    const lblBC = document.getElementById('lblBC');
    const reflAxis = document.getElementById('reflAxis');
    const reflLabel = document.getElementById('reflLabel');
    const badge = document.getElementById('badge');
    const stepDesc = document.getElementById('stepDesc');
    const playBtn = document.getElementById('playBtn');
    const stepBtns = document.querySelectorAll('[data-step]');

    function updateRightAngleMark(A, B, C) {
      const v1x = B.x - A.x, v1y = B.y - A.y;
      const len1 = Math.hypot(v1x, v1y) || 1;
      const u1x = (v1x / len1) * 14, u1y = (v1y / len1) * 14;

      const v2x = C.x - A.x, v2y = C.y - A.y;
      const len2 = Math.hypot(v2x, v2y) || 1;
      const u2x = (v2x / len2) * 14, u2y = (v2y / len2) * 14;

      const p1x = A.x + u1x, p1y = A.y + u1y;
      const p2x = A.x + u1x + u2x, p2y = A.y + u1y + u2y;
      const p3x = A.x + u2x, p3y = A.y + u2y;

      rightAngleMark.setAttribute('d', `M ${p1x} ${p1y} L ${p2x} ${p2y} L ${p3x} ${p3y}`);
    }

    function render() {
      const pts = `${cur.A.x},${cur.A.y} ${cur.B.x},${cur.B.y} ${cur.C.x},${cur.C.y}`;
      polyABC.setAttribute('points', pts);
      glowPoly.setAttribute('points', pts);
      glowPoly.setAttribute('opacity', glowOpacity);

      updateRightAngleMark(cur.A, cur.B, cur.C);

      dotA.setAttribute('cx', cur.A.x);
      dotA.setAttribute('cy', cur.A.y);
      dotB.setAttribute('cx', cur.B.x);
      dotB.setAttribute('cy', cur.B.y);
      dotC.setAttribute('cx', cur.C.x);
      dotC.setAttribute('cy', cur.C.y);

      txtA.setAttribute('x', cur.txtA.x);
      txtA.setAttribute('y', cur.txtA.y);
      txtB.setAttribute('x', cur.txtB.x);
      txtB.setAttribute('y', cur.txtB.y);
      txtC.setAttribute('x', cur.txtC.x);
      txtC.setAttribute('y', cur.txtC.y);

      lblAB.setAttribute('x', cur.lblAB.x);
      lblAB.setAttribute('y', cur.lblAB.y);
      lblAC.setAttribute('x', cur.lblAC.x);
      lblAC.setAttribute('y', cur.lblAC.y);
      lblBC.setAttribute('x', cur.lblBC.x);
      lblBC.setAttribute('y', cur.lblBC.y);

      reflAxis.setAttribute('opacity', curRefl);
      reflLabel.setAttribute('opacity', curRefl);
    }

    function easeInOutCubic(t) {
      return t < 0.5 ? 4 * t * t * t : 1 - Math.pow(-2 * t + 2, 3) / 2;
    }

    function animateTo(targetIndex, duration = 750) {
      if (animFrame) cancelAnimationFrame(animFrame);

      current = targetIndex;
      stepBtns.forEach((b, i) => b.classList.toggle('active', i === current));
      stepDesc.textContent = states[current].desc;

      const target = states[current];
      const startState = JSON.parse(JSON.stringify(cur));
      const startRefl = curRefl;
      const targetRefl = target.refl;

      const startTime = performance.now();

      function update(now) {
        const elapsed = now - startTime;
        const progress = Math.min(1, elapsed / duration);
        const ease = easeInOutCubic(progress);

        // Interpolate points
        ['A', 'B', 'C', 'txtA', 'txtB', 'txtC', 'lblAB', 'lblAC', 'lblBC'].forEach(k => {
          cur[k].x = startState[k].x + (target[k].x - startState[k].x) * ease;
          cur[k].y = startState[k].y + (target[k].y - startState[k].y) * ease;
        });

        curRefl = startRefl + (targetRefl - startRefl) * ease;

        if (current === 3 && progress > 0.8) {
          glowOpacity = Math.sin((progress - 0.8) / 0.2 * Math.PI) * 0.85;
        } else {
          glowOpacity = Math.max(0, glowOpacity - 0.05);
        }

        render();

        if (progress < 1) {
          animFrame = requestAnimationFrame(update);
        } else {
          // Finalize state values exactly
          ['A', 'B', 'C', 'txtA', 'txtB', 'txtC', 'lblAB', 'lblAC', 'lblBC'].forEach(k => {
            cur[k].x = target[k].x;
            cur[k].y = target[k].y;
          });
          curRefl = targetRefl;

          if (current === 3) {
            badge.classList.add('visible');
            triggerGlowPulse();
          } else {
            badge.classList.remove('visible');
            glowOpacity = 0;
            render();
          }
        }
      }

      if (current !== 3) {
        badge.classList.remove('visible');
      }

      animFrame = requestAnimationFrame(update);
    }

    function triggerGlowPulse() {
      let startTime = performance.now();
      function pulse(now) {
        let t = (now - startTime) / 600;
        if (t <= 1) {
          glowOpacity = Math.sin(t * Math.PI) * 0.9;
          render();
          requestAnimationFrame(pulse);
        } else {
          glowOpacity = 0;
          render();
        }
      }
      requestAnimationFrame(pulse);
    }

    function nextStep() {
      const next = (current + 1) % states.length;
      animateTo(next, next === 0 ? 500 : 800);
    }

    function startAutoPlay() {
      playing = true;
      playBtn.textContent = '⏸';
      if (autoTimer) clearInterval(autoTimer);
      autoTimer = setInterval(nextStep, 2800);
    }

    function stopAutoPlay() {
      playing = false;
      playBtn.textContent = '▶';
      if (autoTimer) {
        clearInterval(autoTimer);
        autoTimer = null;
      }
    }

    playBtn.addEventListener('click', () => {
      if (playing) {
        stopAutoPlay();
      } else {
        nextStep();
        startAutoPlay();
      }
    });

    stepBtns.forEach((btn, idx) => {
      btn.addEventListener('click', () => {
        stopAutoPlay();
        animateTo(idx);
      });
    });

    // Initial render and start
    render();
    startAutoPlay();
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      width: 100%;
      height: 100%;
      background: #ffffff;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      padding: 10px;
      user-select: none;
    }

    .graph-container {
      width: 100%;
      max-width: 420px;
      flex: 1;
      display: flex;
      align-items: center;
      justify-content: center;
      min-height: 0;
    }

    svg {
      width: 100%;
      height: auto;
      max-height: 380px;
      display: block;
      overflow: visible;
    }

    .controls {
      width: 100%;
      max-width: 420px;
      display: flex;
      flex-direction: column;
      gap: 8px;
      padding: 4px 8px 0 8px;
    }

    .slider-row {
      display: flex;
      align-items: center;
      gap: 12px;
    }

    .k-badge {
      font-weight: 700;
      font-size: 15px;
      color: #7c3aed;
      min-width: 58px;
    }

    input[type="range"] {
      flex: 1;
      height: 6px;
      border-radius: 3px;
      background: #e2e8f0;
      outline: none;
      -webkit-appearance: none;
      appearance: none;
      cursor: pointer;
    }

    input[type="range"]::-webkit-slider-thumb {
      -webkit-appearance: none;
      appearance: none;
      width: 20px;
      height: 20px;
      border-radius: 50%;
      background: #7c3aed;
      cursor: pointer;
      box-shadow: 0 1px 4px rgba(124, 58, 237, 0.4);
    }

    input[type="range"]::-moz-range-thumb {
      width: 20px;
      height: 20px;
      border-radius: 50%;
      background: #7c3aed;
      cursor: pointer;
      border: none;
      box-shadow: 0 1px 4px rgba(124, 58, 237, 0.4);
    }

    .btn-row {
      display: flex;
      justify-content: center;
      gap: 8px;
    }

    .preset-btn {
      flex: 1;
      padding: 6px 0;
      border: 1px solid #cbd5e1;
      background: #f8fafc;
      border-radius: 6px;
      font-size: 13px;
      font-weight: 600;
      color: #475569;
      cursor: pointer;
      transition: background 0.15s, border-color 0.15s, color 0.15s;
    }

    .preset-btn.active {
      background: #7c3aed;
      border-color: #7c3aed;
      color: #ffffff;
    }

    .grid-line { stroke: #e2e8f0; stroke-width: 1; }
    .axis-line { stroke: #94a3b8; stroke-width: 1.5; }
    .axis-num { font-size: 11px; fill: #64748b; font-family: monospace; }
    .ray-line { stroke: #fb923c; stroke-width: 1.5; stroke-dasharray: 4 3; opacity: 0.85; }
    
    .tri-original {
      fill: rgba(37, 99, 235, 0.15);
      stroke: #2563eb;
      stroke-width: 2;
    }

    .tri-dilated {
      fill: rgba(124, 58, 237, 0.2);
      stroke: #7c3aed;
      stroke-width: 2.5;
    }

    .point-orig { fill: #2563eb; }
    .point-dil { fill: #7c3aed; }
    .point-origin { fill: #1e2945; }

    .label-orig { font-size: 11px; font-weight: 700; fill: #1d4ed8; }
    .label-dil { font-size: 11px; font-weight: 700; fill: #6d28d9; }
  </style>
</head>
<body>

  <div class="graph-container">
    <svg id="svgGraph" viewBox="0 0 400 420">
      <defs>
        <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse">
          <path d="M 40 0 L 0 0 0 40" fill="none" class="grid-line" />
        </pattern>
      </defs>

      
      <g id="gridGroup"></g>

      
      <line id="rayA" x1="40" y1="380" x2="380" y2="40" class="ray-line" />
      <line id="rayB" x1="40" y1="380" x2="380" y2="266.67" class="ray-line" />
      <line id="rayC" x1="40" y1="380" x2="130" y2="20" class="ray-line" />

      
      <polygon id="origTri" class="tri-original" points="80,340 160,340 80,220" />

      
      <polygon id="dilTri" class="tri-dilated" points="80,340 160,340 80,220" />

      
      <circle cx="40" cy="380" r="4" class="point-origin" />
      <text x="32" y="396" font-size="11" font-weight="700" fill="#1e2945">O(0,0)</text>

      
      <g id="origPoints">
        <circle cx="80" cy="340" r="3.5" class="point-orig" />
        <circle cx="160" cy="340" r="3.5" class="point-orig" />
        <circle cx="80" cy="220" r="3.5" class="point-orig" />
        <text id="lblA" x="85" y="355" class="label-orig">A(1,1)</text>
        <text id="lblB" x="165" y="355" class="label-orig">B(3,1)</text>
        <text id="lblC" x="50" y="215" class="label-orig">C(1,4)</text>
      </g>

      
      <g id="dilPoints">
        <circle id="ptA" cx="80" cy="340" r="4" class="point-dil" />
        <circle id="ptB" cx="160" cy="340" r="4" class="point-dil" />
        <circle id="ptC" cx="80" cy="220" r="4" class="point-dil" />
        <text id="lblAdil" x="85" y="335" class="label-dil">A'</text>
        <text id="lblBdil" x="165" y="335" class="label-dil">B'</text>
        <text id="lblCdil" x="88" y="215" class="label-dil">C'</text>
      </g>
    </svg>
  </div>

  <div class="controls">
    <div class="slider-row">
      <span class="k-badge" id="kBadge">k = 1.0</span>
      <input type="range" id="kSlider" min="1" max="2" step="0.01" value="1">
    </div>
    <div class="btn-row">
      <button class="preset-btn active" id="btn1">k = 1</button>
      <button class="preset-btn" id="btn15">k = 1.5</button>
      <button class="preset-btn" id="btn2">k = 2</button>
      <button class="preset-btn" id="btnAnim">▶ Play</button>
    </div>
  </div>

  <script>
    const originX = 40, originY = 380, scale = 40;

    function toSvg(x, y) {
      return { x: originX + x * scale, y: originY - y * scale };
    }

    // Generate grid & axes
    const gridGroup = document.getElementById('gridGroup');
    let gridSvg = '';
    for (let x = 0; x <= 8; x++) {
      const pos = toSvg(x, 0).x;
      gridSvg += `<line x1="${pos}" y1="20" x2="${pos}" y2="380" class="grid-line" />`;
      gridSvg += `<text x="${pos}" y="396" text-anchor="middle" class="axis-num">${x}</text>`;
    }
    for (let y = 0; y <= 9; y++) {
      const pos = toSvg(0, y).y;
      gridSvg += `<line x1="40" y1="${pos}" x2="360" y2="${pos}" class="grid-line" />`;
      if (y > 0) {
        gridSvg += `<text x="32" y="${pos + 4}" text-anchor="end" class="axis-num">${y}</text>`;
      }
    }
    gridSvg += `<line x1="40" y1="380" x2="375" y2="380" class="axis-line" marker-end="url(#arrow)" />`;
    gridSvg += `<line x1="40" y1="380" x2="40" y2="10" class="axis-line" marker-end="url(#arrow)" />`;
    gridSvg += `<text x="375" y="396" class="axis-num" font-weight="bold">x</text>`;
    gridSvg += `<text x="28" y="15" class="axis-num" font-weight="bold">y</text>`;
    gridGroup.innerHTML = gridSvg;

    const dilTri = document.getElementById('dilTri');
    const ptA = document.getElementById('ptA');
    const ptB = document.getElementById('ptB');
    const ptC = document.getElementById('ptC');
    const lblAdil = document.getElementById('lblAdil');
    const lblBdil = document.getElementById('lblBdil');
    const lblCdil = document.getElementById('lblCdil');
    const kSlider = document.getElementById('kSlider');
    const kBadge = document.getElementById('kBadge');

    const btn1 = document.getElementById('btn1');
    const btn15 = document.getElementById('btn15');
    const btn2 = document.getElementById('btn2');
    const btnAnim = document.getElementById('btnAnim');

    function updateScale(k) {
      kBadge.textContent = `k = ${k.toFixed(1)}`;
      kSlider.value = k;

      const a = toSvg(1 * k, 1 * k);
      const b = toSvg(3 * k, 1 * k);
      const c = toSvg(1 * k, 4 * k);

      dilTri.setAttribute('points', `${a.x},${a.y} ${b.x},${b.y} ${c.x},${c.y}`);
      
      ptA.setAttribute('cx', a.x);
      ptA.setAttribute('cy', a.y);
      ptB.setAttribute('cx', b.x);
      ptB.setAttribute('cy', b.y);
      ptC.setAttribute('cx', c.x);
      ptC.setAttribute('cy', c.y);

      const ax = (1 * k).toFixed(k % 1 === 0 ? 0 : 1);
      const ay = (1 * k).toFixed(k % 1 === 0 ? 0 : 1);
      const bx = (3 * k).toFixed(k % 1 === 0 ? 0 : 1);
      const by = (1 * k).toFixed(k % 1 === 0 ? 0 : 1);
      const cx = (1 * k).toFixed(k % 1 === 0 ? 0 : 1);
      const cy = (4 * k).toFixed(k % 1 === 0 ? 0 : 1);

      if (k === 1) {
        lblAdil.textContent = "";
        lblBdil.textContent = "";
        lblCdil.textContent = "";
      } else {
        lblAdil.textContent = `A'(${ax},${ay})`;
        lblAdil.setAttribute('x', a.x + 8);
        lblAdil.setAttribute('y', a.y - 6);

        lblBdil.textContent = `B'(${bx},${by})`;
        lblBdil.setAttribute('x', b.x + 8);
        lblBdil.setAttribute('y', b.y - 6);

        lblCdil.textContent = `C'(${cx},${cy})`;
        lblCdil.setAttribute('x', c.x + 8);
        lblCdil.setAttribute('y', c.y - 6);
      }

      [btn1, btn15, btn2].forEach(btn => btn.classList.remove('active'));
      if (Math.abs(k - 1) < 0.02) btn1.classList.add('active');
      else if (Math.abs(k - 1.5) < 0.02) btn15.classList.add('active');
      else if (Math.abs(k - 2) < 0.02) btn2.classList.add('active');
    }

    let animTimer = null;

    function animateTo(targetK) {
      clearInterval(animTimer);
      const startK = parseFloat(kSlider.value);
      const duration = 400;
      const startTime = performance.now();

      animTimer = setInterval(() => {
        const elapsed = performance.now() - startTime;
        const progress = Math.min(1, elapsed / duration);
        const ease = 0.5 - Math.cos(progress * Math.PI) / 2;
        const currentK = startK + (targetK - startK) * ease;
        updateScale(currentK);
        if (progress >= 1) clearInterval(animTimer);
      }, 16);
    }

    let isPlaying = false;
    let playInterval = null;

    function togglePlay() {
      if (isPlaying) {
        stopPlay();
      } else {
        isPlaying = true;
        btnAnim.textContent = '⏸ Pause';
        btnAnim.classList.add('active');
        let forward = parseFloat(kSlider.value) < 1.9;
        
        playInterval = setInterval(() => {
          let curr = parseFloat(kSlider.value);
          if (forward) {
            curr += 0.02;
            if (curr >= 2) { curr = 2; forward = false; }
          } else {
            curr -= 0.02;
            if (curr <= 1) { curr = 1; forward = true; }
          }
          updateScale(curr);
        }, 30);
      }
    }

    function stopPlay() {
      isPlaying = false;
      clearInterval(playInterval);
      btnAnim.textContent = '▶ Play';
      btnAnim.classList.remove('active');
    }

    kSlider.addEventListener('input', (e) => {
      stopPlay();
      updateScale(parseFloat(e.target.value));
    });

    btn1.addEventListener('click', () => { stopPlay(); animateTo(1); });
    btn15.addEventListener('click', () => { stopPlay(); animateTo(1.5); });
    btn2.addEventListener('click', () => { stopPlay(); animateTo(2); });
    btnAnim.addEventListener('click', togglePlay);

    updateScale(1);
  </script>
</body>
</html>

Dilations with Center at Origin and Scale Factor k

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      background: #ffffff;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
    }

    .main-layout {
      display: flex;
      flex-direction: row;
      flex-wrap: wrap;
      gap: 16px;
      width: 100%;
      max-width: 640px;
      align-items: center;
      justify-content: center;
    }

    .graph-container {
      flex: 1 1 280px;
      max-width: 320px;
      aspect-ratio: 1 / 1;
      position: relative;
    }

    svg {
      width: 100%;
      height: 100%;
      display: block;
      overflow: visible;
    }

    .panel {
      flex: 1 1 240px;
      display: flex;
      flex-direction: column;
      gap: 8px;
    }

    .formula-badge {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      border-radius: 8px;
      padding: 6px 10px;
      text-align: center;
      font-weight: 700;
      font-size: 15px;
      color: #0f172a;
    }

    .formula-badge span.k-factor {
      color: #ea580c;
    }

    .vertex-list {
      display: flex;
      flex-direction: column;
      gap: 6px;
    }

    .vertex-row {
      display: flex;
      align-items: center;
      justify-content: space-between;
      padding: 6px 10px;
      border-radius: 6px;
      border: 1px solid #e2e8f0;
      background: #f8fafc;
      font-size: 13px;
      cursor: pointer;
      transition: all 0.2s ease;
      user-select: none;
    }

    .vertex-row.active {
      border-color: #ea580c;
      background: #fff7ed;
      box-shadow: 0 0 0 1px #ea580c;
    }

    .vertex-label-teal {
      font-weight: 700;
      color: #0f766e;
    }

    .vertex-label-orange {
      font-weight: 700;
      color: #ea580c;
    }

    .arrow {
      color: #94a3b8;
      font-weight: bold;
    }

    .controls {
      display: flex;
      gap: 6px;
      margin-top: 4px;
    }

    .btn {
      flex: 1;
      padding: 6px 10px;
      border-radius: 6px;
      border: 1px solid #cbd5e1;
      background: #ffffff;
      color: #334155;
      font-size: 12px;
      font-weight: 600;
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 4px;
      transition: background 0.15s ease;
    }

    .btn:hover {
      background: #f1f5f9;
    }

    .btn.active {
      background: #0f172a;
      color: #ffffff;
      border-color: #0f172a;
    }

    /* SVG styles */
    .grid-line { stroke: #f1f5f9; stroke-width: 1; }
    .axis-line { stroke: #64748b; stroke-width: 1.5; }
    .axis-tick { stroke: #64748b; stroke-width: 1; }
    .axis-text { font-size: 10px; fill: #64748b; font-family: monospace; }
    
    .ray { stroke: #94a3b8; stroke-width: 1.5; stroke-dasharray: 4 3; opacity: 0.6; transition: all 0.25s ease; }
    .ray.highlight { stroke: #ea580c; stroke-width: 2.5; stroke-dasharray: none; opacity: 1; }

    .poly-orig { fill: rgba(13, 148, 136, 0.12); stroke: #0d9488; stroke-width: 2; }
    .poly-img { fill: rgba(234, 88, 12, 0.2); stroke: #ea580c; stroke-width: 2; stroke-dasharray: 3 2; }

    .point-orig { fill: #0d9488; stroke: #ffffff; stroke-width: 1.5; transition: transform 0.2s ease; }
    .point-img { fill: #ea580c; stroke: #ffffff; stroke-width: 1.5; transition: transform 0.2s ease; }
    
    .pt-highlight { stroke: #0f172a; stroke-width: 2; }
    
    .pt-text { font-size: 10px; font-weight: 700; font-family: system-ui, sans-serif; }
    .pt-text-orig { fill: #0f766e; }
    .pt-text-img { fill: #ea580c; }
  </style>
</head>
<body>

  <div class="main-layout">
    
    <div class="graph-container">
      <svg viewBox="-5 -5 320 320" id="graph">
        <defs>
          <marker id="arrow" viewBox="0 0 10 10" refX="5" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
            <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#64748b"/>
          </marker>
        </defs>

        
        
        <g id="grid">
          
          <line x1="30" y1="270" x2="282" y2="270" class="grid-line"/>
          <line x1="30" y1="234" x2="282" y2="234" class="grid-line"/>
          <line x1="30" y1="198" x2="282" y2="198" class="grid-line"/>
          <line x1="30" y1="162" x2="282" y2="162" class="grid-line"/>
          <line x1="30" y1="126" x2="282" y2="126" class="grid-line"/>
          <line x1="30" y1="90" x2="282" y2="90" class="grid-line"/>
          <line x1="30" y1="54" x2="282" y2="54" class="grid-line"/>
          <line x1="30" y1="18" x2="282" y2="18" class="grid-line"/>

          
          <line x1="30" y1="270" x2="30" y2="18" class="grid-line"/>
          <line x1="66" y1="270" x2="66" y2="18" class="grid-line"/>
          <line x1="102" y1="270" x2="102" y2="18" class="grid-line"/>
          <line x1="138" y1="270" x2="138" y2="18" class="grid-line"/>
          <line x1="174" y1="270" x2="174" y2="18" class="grid-line"/>
          <line x1="210" y1="270" x2="210" y2="18" class="grid-line"/>
          <line x1="246" y1="270" x2="246" y2="18" class="grid-line"/>
          <line x1="282" y1="270" x2="282" y2="18" class="grid-line"/>
        </g>

        
        
        <line id="ray-P" x1="30" y1="270" x2="102" y2="54" class="ray"/>
        
        <line id="ray-Q" x1="30" y1="270" x2="246" y2="54" class="ray"/>
        
        <line id="ray-R" x1="30" y1="270" x2="246" y2="198" class="ray"/>
        
        <line id="ray-S" x1="30" y1="270" x2="102" y2="198" class="ray"/>

        
        <polygon points="102,54 246,54 246,198 102,198" class="poly-orig"/>

        
        <polygon points="66,162 138,162 138,234 66,234" class="poly-img"/>

        
        
        <circle cx="30" cy="270" r="3.5" fill="#1e2945"/>
        <text x="20" y="284" class="axis-text" font-weight="bold">O</text>

        
        <circle id="pt-P" cx="102" cy="54" r="4.5" class="point-orig"/>
        <text x="96" y="44" class="pt-text pt-text-orig">P(2,6)</text>

        <circle id="pt-Q" cx="246" cy="54" r="4.5" class="point-orig"/>
        <text x="248" y="44" class="pt-text pt-text-orig">Q(6,6)</text>

        <circle id="pt-R" cx="246" cy="198" r="4.5" class="point-orig"/>
        <text x="252" y="202" class="pt-text pt-text-orig">R(6,2)</text>

        <circle id="pt-S" cx="102" cy="198" r="4.5" class="point-orig"/>
        <text x="108" y="210" class="pt-text pt-text-orig">S(2,2)</text>

        
        <circle id="pt-Pp" cx="66" cy="162" r="4" class="point-img"/>
        <text x="44" y="156" class="pt-text pt-text-img">P'(1,3)</text>

        <circle id="pt-Qp" cx="138" cy="162" r="4" class="point-img"/>
        <text x="142" y="156" class="pt-text pt-text-img">Q'(3,3)</text>

        <circle id="pt-Rp" cx="138" cy="234" r="4" class="point-img"/>
        <text x="144" y="244" class="pt-text pt-text-img">R'(3,1)</text>

        <circle id="pt-Sp" cx="66" cy="234" r="4" class="point-img"/>
        <text x="42" y="246" class="pt-text pt-text-img">S'(1,1)</text>

        
        <line x1="30" y1="270" x2="295" y2="270" class="axis-line" marker-end="url(#arrow)"/>
        <line x1="30" y1="270" x2="30" y2="8" class="axis-line" marker-end="url(#arrow)"/>

        
        
        <text x="66" y="284" text-anchor="middle" class="axis-text">1</text>
        <text x="102" y="284" text-anchor="middle" class="axis-text">2</text>
        <text x="138" y="284" text-anchor="middle" class="axis-text">3</text>
        <text x="174" y="284" text-anchor="middle" class="axis-text">4</text>
        <text x="210" y="284" text-anchor="middle" class="axis-text">5</text>
        <text x="246" y="284" text-anchor="middle" class="axis-text">6</text>
        <text x="282" y="284" text-anchor="middle" class="axis-text">7</text>
        <text x="302" y="274" class="axis-text" font-weight="bold">x</text>

        
        <text x="22" y="238" text-anchor="end" class="axis-text">1</text>
        <text x="22" y="202" text-anchor="end" class="axis-text">2</text>
        <text x="22" y="166" text-anchor="end" class="axis-text">3</text>
        <text x="22" y="130" text-anchor="end" class="axis-text">4</text>
        <text x="22" y="94" text-anchor="end" class="axis-text">5</text>
        <text x="22" y="58" text-anchor="end" class="axis-text">6</text>
        <text x="22" y="22" text-anchor="end" class="axis-text">7</text>
        <text x="26" y="4" class="axis-text" font-weight="bold">y</text>
      </svg>
    </div>

    
    <div class="panel">
      <div class="formula-badge">
        Rule: (x, y) → (<span class="k-factor">½</span>x, <span class="k-factor">½</span>y)
      </div>

      <div class="vertex-list">
        <div class="vertex-row active" data-vertex="P">
          <span class="vertex-label-teal">P (2, 6)</span>
          <span class="arrow">→ (²⁄₂, ⁶⁄₂) →</span>
          <span class="vertex-label-orange">P' (1, 3)</span>
        </div>

        <div class="vertex-row" data-vertex="Q">
          <span class="vertex-label-teal">Q (6, 6)</span>
          <span class="arrow">→ (⁶⁄₂, ⁶⁄₂) →</span>
          <span class="vertex-label-orange">Q' (3, 3)</span>
        </div>

        <div class="vertex-row" data-vertex="R">
          <span class="vertex-label-teal">R (6, 2)</span>
          <span class="arrow">→ (⁶⁄₂, ²⁄₂) →</span>
          <span class="vertex-label-orange">R' (3, 1)</span>
        </div>

        <div class="vertex-row" data-vertex="S">
          <span class="vertex-label-teal">S (2, 2)</span>
          <span class="arrow">→ (²⁄₂, ²⁄₂) →</span>
          <span class="vertex-label-orange">S' (1, 1)</span>
        </div>
      </div>

      <div class="controls">
        <button class="btn active" id="autoBtn">▶ Auto Step</button>
        <button class="btn" id="allBtn">✦ Show All</button>
      </div>
    </div>
  </div>

  <script>
    const vertices = ['P', 'Q', 'R', 'S'];
    let currentIndex = 0;
    let autoInterval = null;
    let isAll = false;

    const rows = document.querySelectorAll('.vertex-row');
    const autoBtn = document.getElementById('autoBtn');
    const allBtn = document.getElementById('allBtn');

    function setActiveVertex(key) {
      isAll = false;
      allBtn.classList.remove('active');

      rows.forEach(row => {
        const match = row.getAttribute('data-vertex') === key;
        row.classList.toggle('active', match);
      });

      vertices.forEach(v => {
        const isMatch = v === key;
        const ray = document.getElementById(`ray-${v}`);
        const pt = document.getElementById(`pt-${v}`);
        const ptp = document.getElementById(`pt-${v}p`);

        if (ray) ray.classList.toggle('highlight', isMatch);
        if (pt) pt.classList.toggle('pt-highlight', isMatch);
        if (ptp) ptp.classList.toggle('pt-highlight', isMatch);
      });
    }

    function showAll() {
      stopAuto();
      isAll = true;
      allBtn.classList.add('active');
      autoBtn.classList.remove('active');
      autoBtn.textContent = '▶ Auto Step';

      rows.forEach(row => row.classList.remove('active'));
      vertices.forEach(v => {
        const ray = document.getElementById(`ray-${v}`);
        const pt = document.getElementById(`pt-${v}`);
        const ptp = document.getElementById(`pt-${v}p`);
        if (ray) ray.classList.add('highlight');
        if (pt) pt.classList.remove('pt-highlight');
        if (ptp) ptp.classList.remove('pt-highlight');
      });
    }

    function nextStep() {
      currentIndex = (currentIndex + 1) % vertices.length;
      setActiveVertex(vertices[currentIndex]);
    }

    function startAuto() {
      if (autoInterval) clearInterval(autoInterval);
      autoBtn.classList.add('active');
      autoBtn.textContent = '⏸ Pause';
      allBtn.classList.remove('active');
      setActiveVertex(vertices[currentIndex]);
      autoInterval = setInterval(nextStep, 3200);
    }

    function stopAuto() {
      if (autoInterval) {
        clearInterval(autoInterval);
        autoInterval = null;
      }
      autoBtn.classList.remove('active');
      autoBtn.textContent = '▶ Auto Step';
    }

    // Interactive Row clicks
    rows.forEach((row, idx) => {
      row.addEventListener('click', () => {
        stopAuto();
        currentIndex = idx;
        setActiveVertex(row.getAttribute('data-vertex'));
      });
    });

    // Control buttons
    autoBtn.addEventListener('click', () => {
      if (autoInterval) {
        stopAuto();
      } else {
        startAuto();
      }
    });

    allBtn.addEventListener('click', () => {
      showAll();
    });

    // Start auto loop on load
    startAuto();
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1">
  <title>Dilation from Origin</title>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; font-family: system-ui, -apple-system, sans-serif; }
    body {
      background: #f8fafc;
      color: #1e293b;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
      padding: 12px;
      user-select: none;
      -webkit-user-select: none;
    }

    .main-wrap {
      width: 100%;
      max-width: 360px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 10px;
    }

    /* Coordinate Frame */
    .svg-container {
      width: 100%;
      background: #ffffff;
      border-radius: 12px;
      border: 1px solid #e2e8f0;
      box-shadow: 0 1px 3px rgba(0,0,0,0.04);
      display: flex;
      justify-content: center;
      align-items: center;
    }

    svg {
      width: 100%;
      height: auto;
      display: block;
    }

    /* Equation / Step Flow */
    .rule-card {
      width: 100%;
      display: flex;
      align-items: center;
      justify-content: space-between;
      gap: 6px;
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 10px;
      padding: 8px 10px;
      font-size: 13px;
      font-weight: 600;
    }

    .chip {
      padding: 4px 8px;
      border-radius: 6px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 2px;
      line-height: 1.1;
    }

    .chip-label {
      font-size: 10px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
    }

    .chip-p {
      background: #eff6ff;
      color: #2563eb;
      border: 1px solid #bfdbfe;
    }

    .chip-k {
      background: #f8fafc;
      color: #475569;
      border: 1px solid #cbd5e1;
    }

    .chip-prime {
      background: #f5f3ff;
      color: #7c3aed;
      border: 1px solid #ddd6fe;
    }

    .arrow {
      color: #94a3b8;
      font-size: 14px;
      font-weight: bold;
    }

    /* Controls */
    .controls {
      display: flex;
      align-items: center;
      gap: 6px;
      width: 100%;
      justify-content: center;
    }

    .btn-k {
      flex: 1;
      padding: 6px 0;
      background: #ffffff;
      border: 1.5px solid #cbd5e1;
      border-radius: 8px;
      font-size: 13px;
      font-weight: 700;
      color: #475569;
      cursor: pointer;
      transition: all 0.2s ease;
    }

    .btn-k.active {
      background: #7c3aed;
      border-color: #7c3aed;
      color: #ffffff;
      box-shadow: 0 2px 6px rgba(124, 58, 237, 0.25);
    }
  </style>
</head>
<body>

<div class="main-wrap">
  
  <div class="svg-container">
    <svg viewBox="0 0 320 260">
      <defs>
        <marker id="arrow" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
          <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#94a3b8" />
        </marker>
        <marker id="ray-arrow" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
          <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#a855f7" />
        </marker>
      </defs>

      
      
      <g stroke="#f1f5f9" stroke-width="1.5">
        
        <line x1="67" y1="25" x2="67" y2="225" />
        <line x1="99" y1="25" x2="99" y2="225" />
        <line x1="131" y1="25" x2="131" y2="225" />
        <line x1="163" y1="25" x2="163" y2="225" />
        <line x1="195" y1="25" x2="195" y2="225" />
        <line x1="227" y1="25" x2="227" y2="225" />
        <line x1="259" y1="25" x2="259" y2="225" />
        <line x1="291" y1="25" x2="291" y2="225" />

        
        <line x1="35" y1="193" x2="300" y2="193" />
        <line x1="35" y1="161" x2="300" y2="161" />
        <line x1="35" y1="129" x2="300" y2="129" />
        <line x1="35" y1="97" x2="300" y2="97" />
        <line x1="35" y1="65" x2="300" y2="65" />
        <line x1="35" y1="33" x2="300" y2="33" />
      </g>

      
      
      <line x1="35" y1="225" x2="305" y2="225" stroke="#94a3b8" stroke-width="2" marker-end="url(#arrow)" />
      
      <line x1="35" y1="225" x2="35" y2="15" stroke="#94a3b8" stroke-width="2" marker-end="url(#arrow)" />

      
      <text x="35" y="242" font-size="11" fill="#64748b" text-anchor="middle" font-weight="600">0</text>
      <text x="67" y="242" font-size="11" fill="#64748b" text-anchor="middle">1</text>
      <text x="99" y="242" font-size="11" fill="#64748b" text-anchor="middle" font-weight="600">2</text>
      <text x="131" y="242" font-size="11" fill="#64748b" text-anchor="middle">3</text>
      <text x="163" y="242" font-size="11" fill="#64748b" text-anchor="middle" font-weight="600">4</text>
      <text x="195" y="242" font-size="11" fill="#64748b" text-anchor="middle">5</text>
      <text x="227" y="242" font-size="11" fill="#64748b" text-anchor="middle" font-weight="600">6</text>
      <text x="259" y="242" font-size="11" fill="#64748b" text-anchor="middle">7</text>
      <text x="305" y="242" font-size="12" fill="#64748b" font-weight="700">x</text>

      <text x="22" y="197" font-size="11" fill="#64748b" text-anchor="middle">1</text>
      <text x="22" y="165" font-size="11" fill="#64748b" text-anchor="middle">2</text>
      <text x="22" y="133" font-size="11" fill="#64748b" text-anchor="middle" font-weight="600">3</text>
      <text x="22" y="101" font-size="11" fill="#64748b" text-anchor="middle">4</text>
      <text x="22" y="69" font-size="11" fill="#64748b" text-anchor="middle">5</text>
      <text x="22" y="37" font-size="11" fill="#64748b" text-anchor="middle" font-weight="600">6</text>
      <text x="22" y="15" font-size="12" fill="#64748b" font-weight="700">y</text>

      
      
      <line x1="35" y1="225" x2="175" y2="15" stroke="#c084fc" stroke-width="2" stroke-dasharray="5 4" marker-end="url(#ray-arrow)" />

      
      <circle cx="35" cy="225" r="4.5" fill="#64748b" />
      <text x="44" y="220" font-size="11" font-weight="700" fill="#475569">(0,0)</text>

      
      
      <line x1="99" y1="225" x2="99" y2="129" stroke="#93c5fd" stroke-width="1.5" stroke-dasharray="3 3" />
      <line x1="35" y1="129" x2="99" y2="129" stroke="#93c5fd" stroke-width="1.5" stroke-dasharray="3 3" />
      <circle cx="99" cy="129" r="6" fill="#2563eb" />
      <text x="110" y="134" font-size="12" font-weight="700" fill="#2563eb">P (2, 3)</text>

      
      <g id="primeGroup">
        
        <line id="projX" x1="163" y1="225" x2="163" y2="33" stroke="#ddd6fe" stroke-width="1.5" stroke-dasharray="3 3" />
        <line id="projY" x1="35" y1="33" x2="163" y2="33" stroke="#ddd6fe" stroke-width="1.5" stroke-dasharray="3 3" />
        
        <circle id="dotPrime" cx="163" cy="33" r="6.5" fill="#7c3aed" />
        <text id="lblPrime" x="175" y="38" font-size="12" font-weight="800" fill="#7c3aed">P' (4, 6)</text>
      </g>
    </svg>
  </div>

  
  <div class="rule-card">
    <div class="chip chip-p">
      <span class="chip-label">Original</span>
      <span>(2, 3)</span>
    </div>
    <span class="arrow">→</span>
    <div class="chip chip-k">
      <span class="chip-label">Multiply</span>
      <span id="cardK">× k = 2</span>
    </div>
    <span class="arrow">→</span>
    <div class="chip chip-prime">
      <span class="chip-label">Image P'</span>
      <span id="cardPrime">(4, 6)</span>
    </div>
  </div>

  
  <div class="controls">
    <button class="btn-k" onclick="setK(0.5)">k = 0.5</button>
    <button class="btn-k" onclick="setK(1)">k = 1</button>
    <button class="btn-k active" onclick="setK(2)">k = 2</button>
    <button class="btn-k" onclick="setK(2.5)">k = 2.5</button>
  </div>
</div>

<script>
  const ORIGIN_X = 35;
  const ORIGIN_Y = 225;
  const STEP = 32;

  function setK(k) {
    // Update active button
    document.querySelectorAll('.btn-k').forEach(btn => {
      btn.classList.toggle('active', btn.textContent.trim() === 'k = ' + k);
    });

    const px = 2 * k;
    const py = 3 * k;

    const svgX = ORIGIN_X + px * STEP;
    const svgY = ORIGIN_Y - py * STEP;

    // Update Image Point & Projections
    const dotPrime = document.getElementById('dotPrime');
    const lblPrime = document.getElementById('lblPrime');
    const projX = document.getElementById('projX');
    const projY = document.getElementById('projY');

    dotPrime.setAttribute('cx', svgX);
    dotPrime.setAttribute('cy', svgY);

    projX.setAttribute('x1', svgX);
    projX.setAttribute('y1', ORIGIN_Y);
    projX.setAttribute('x2', svgX);
    projX.setAttribute('y2', svgY);

    projY.setAttribute('x1', ORIGIN_X);
    projY.setAttribute('y1', svgY);
    projY.setAttribute('x2', svgX);
    projY.setAttribute('y2', svgY);

    lblPrime.setAttribute('x', svgX + 11);
    lblPrime.setAttribute('y', svgY + 5);
    lblPrime.textContent = `P' (${px}, ${py})`;

    // Adjust text position if near boundary
    if (k === 2.5) {
      lblPrime.setAttribute('x', svgX - 60);
      lblPrime.setAttribute('y', svgY - 8);
    } else if (k === 1) {
      lblPrime.setAttribute('x', svgX + 11);
      lblPrime.setAttribute('y', svgY - 8);
    }

    // Update Cards
    document.getElementById('cardK').textContent = `× k = ${k}`;
    document.getElementById('cardPrime').textContent = `(${px}, ${py})`;
  }
</script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      width: 100%;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      background: transparent;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      padding: 8px 12px;
      user-select: none;
    }
    .diagram-container {
      width: 100%;
      max-width: 480px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 6px;
    }
    .header-tag {
      font-size: 12px;
      font-weight: 600;
      color: #475569;
      text-align: center;
      background: #f1f5f9;
      padding: 3px 10px;
      border-radius: 12px;
    }
    .diagram-area {
      width: 100%;
      display: flex;
      align-items: center;
      justify-content: center;
    }
    svg {
      width: 100%;
      height: auto;
      max-height: 250px;
      display: block;
      overflow: visible;
    }
    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 10px;
      width: 100%;
      padding: 0 4px;
    }
    .btn {
      background: #f8fafc;
      border: 1px solid #e6e6e6;
      border-radius: 6px;
      padding: 6px 12px;
      font-size: 13px;
      font-weight: 600;
      color: #1e2945;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      gap: 4px;
      white-space: nowrap;
      transition: background 0.15s, border-color 0.15s, color 0.15s;
    }
    .btn:hover {
      background: #f1f5f9;
      border-color: #cbd5e1;
    }
    .btn.active {
      background: #4f46e5;
      border-color: #4f46e5;
      color: #ffffff;
    }
    .slider-wrap {
      flex: 1;
      display: flex;
      align-items: center;
      gap: 8px;
    }
    input[type="range"] {
      flex: 1;
      accent-color: #4f46e5;
      cursor: pointer;
      height: 6px;
    }
    .angle-readout {
      font-size: 13px;
      font-weight: 700;
      color: #4f46e5;
      min-width: 44px;
      text-align: right;
      font-variant-numeric: tabular-nums;
    }
    .callout-note {
      font-size: 11.5px;
      color: #64748b;
      text-align: center;
    }
    .highlight-teal { color: #0d9488; font-weight: 600; }
    .highlight-indigo { color: #4f46e5; font-weight: 600; }
  </style>
</head>
<body>

  <div class="diagram-container">
    <div class="header-tag">
      Rotation of 120° Preserves Side Lengths &amp; Angle Measures
    </div>

    <div class="diagram-area">
      <svg viewBox="90 55 390 215" aria-label="Triangle rotating 120 degrees preserving side lengths and angles">
        <defs>
          <marker id="arrow" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
            <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#4f46e5"/>
          </marker>
        </defs>

        
        <circle cx="260" cy="215" r="4" fill="#1e2945"/>
        <text x="260" y="233" text-anchor="middle" font-size="11" font-weight="700" fill="#1e2945">Center</text>

        
        <path id="rotArc" d="M 370 215 A 110 110 0 0 0 205 119.7" fill="none" stroke="#cbd5e1" stroke-width="1.5" stroke-dasharray="3 3"/>
        <path id="progressArc" d="M 370 215 A 110 110 0 0 0 370 215" fill="none" stroke="#4f46e5" stroke-width="2.5" marker-end="url(#arrow)"/>
        <text id="arcLabel" x="330" y="125" font-size="12" font-weight="700" fill="#4f46e5" display="none">120°</text>

        
        <g id="originalStatic" opacity="0.95">
          
          <polygon points="310,215 414,215 310,137" fill="rgba(13,148,136,0.12)" stroke="#0d9488" stroke-width="2" stroke-linejoin="round"/>
          
          
          <path d="M 310 205 L 320 205 L 320 215" fill="none" stroke="#0d9488" stroke-width="1.5"/>

          
          
          <path d="M 392 215 A 22 22 0 0 0 397 202" fill="none" stroke="#0d9488" stroke-width="1.5"/>
          <text x="385" y="209" font-size="10.5" font-weight="700" fill="#0d9488" text-anchor="end">37°</text>

          
          <path d="M 310 157 A 20 20 0 0 0 321 152" fill="none" stroke="#0d9488" stroke-width="1.5"/>
          <text x="323" y="162" font-size="10.5" font-weight="700" fill="#0d9488">53°</text>

          
          <text x="362" y="230" font-size="11.5" font-weight="700" fill="#0d9488" text-anchor="middle">4 cm</text>
          <text x="300" y="180" font-size="11.5" font-weight="700" fill="#0d9488" text-anchor="end">3 cm</text>
          <text x="372" y="168" font-size="11.5" font-weight="700" fill="#0d9488">5 cm</text>
          
          
          <rect x="335" y="244" width="56" height="17" rx="3" fill="#0d9488"/>
          <text x="363" y="256" font-size="9.5" font-weight="700" fill="#ffffff" text-anchor="middle">Original</text>
        </g>

        
        <g id="rotatingGroup" transform="rotate(0 260 215)">
          <polygon points="310,215 414,215 310,137" fill="rgba(79,70,229,0.18)" stroke="#4f46e5" stroke-width="2" stroke-linejoin="round"/>
          
          
          <path d="M 310 205 L 320 205 L 320 215" fill="none" stroke="#4f46e5" stroke-width="1.5"/>

          
          
          <path d="M 392 215 A 22 22 0 0 0 397 202" fill="none" stroke="#4f46e5" stroke-width="1.5"/>
          <text x="385" y="209" font-size="10.5" font-weight="700" fill="#4f46e5" text-anchor="end">37°</text>

          
          <path d="M 310 157 A 20 20 0 0 0 321 152" fill="none" stroke="#4f46e5" stroke-width="1.5"/>
          <text x="323" y="162" font-size="10.5" font-weight="700" fill="#4f46e5">53°</text>

          
          <text x="362" y="230" font-size="11.5" font-weight="700" fill="#4f46e5" text-anchor="middle">4 cm</text>
          <text x="300" y="180" font-size="11.5" font-weight="700" fill="#4f46e5" text-anchor="end">3 cm</text>
          <text x="372" y="168" font-size="11.5" font-weight="700" fill="#4f46e5">5 cm</text>
          
          
          <g id="imageBadge" opacity="0">
            <rect x="335" y="244" width="52" height="17" rx="3" fill="#4f46e5"/>
            <text x="361" y="256" font-size="9.5" font-weight="700" fill="#ffffff" text-anchor="middle">Image</text>
          </g>
        </g>
      </svg>
    </div>

    
    <div class="controls">
      <button id="playBtn" class="btn" aria-label="Play/Pause rotation">▶ Rotate</button>
      <div class="slider-wrap">
        <input type="range" id="angleSlider" min="0" max="120" value="0" step="1" aria-label="Rotation angle">
        <span id="angleText" class="angle-readout">0°</span>
      </div>
    </div>

    <div class="callout-note">
      <span class="highlight-teal">Pre-image</span> and <span class="highlight-indigo">Image</span> remain congruent: lengths (3, 4, 5 cm) and angles (37°, 53°, 90°) are preserved.
    </div>
  </div>

  <script>
    const rotatingGroup = document.getElementById('rotatingGroup');
    const imageBadge = document.getElementById('imageBadge');
    const progressArc = document.getElementById('progressArc');
    const arcLabel = document.getElementById('arcLabel');
    const slider = document.getElementById('angleSlider');
    const angleText = document.getElementById('angleText');
    const playBtn = document.getElementById('playBtn');

    let currentAngle = 0;
    let isPlaying = false;
    let animFrame = null;
    let lastTime = null;

    function describeArc(cx, cy, r, startAngleDeg, endAngleDeg) {
      const rad1 = (startAngleDeg) * Math.PI / 180;
      const rad2 = (endAngleDeg) * Math.PI / 180;
      const x1 = cx + r * Math.cos(rad1);
      const y1 = cy - r * Math.sin(rad1);
      const x2 = cx + r * Math.cos(rad2);
      const y2 = cy - r * Math.sin(rad2);
      const largeArc = (endAngleDeg - startAngleDeg) <= 180 ? 0 : 1;
      return `M ${x1} ${y1} A ${r} ${r} 0 ${largeArc} 0 ${x2} ${y2}`;
    }

    function setAngle(deg) {
      currentAngle = deg;
      slider.value = deg;
      angleText.textContent = Math.round(deg) + '°';

      rotatingGroup.setAttribute('transform', `rotate(${-deg} 260 215)`);
      
      if (deg > 1) {
        progressArc.setAttribute('d', describeArc(260, 215, 110, 0, deg));
        progressArc.style.display = 'inline';
        arcLabel.style.display = 'inline';
        arcLabel.textContent = Math.round(deg) + '°';
        const midRad = (deg / 2) * Math.PI / 180;
        arcLabel.setAttribute('x', 260 + 125 * Math.cos(midRad));
        arcLabel.setAttribute('y', 215 - 125 * Math.sin(midRad));
      } else {
        progressArc.style.display = 'none';
        arcLabel.style.display = 'none';
      }

      imageBadge.setAttribute('opacity', deg > 15 ? '1' : '0');
    }

    function animateLoop(timestamp) {
      if (!lastTime) lastTime = timestamp;
      const dt = (timestamp - lastTime) / 1000;
      lastTime = timestamp;

      if (isPlaying) {
        let next = currentAngle + dt * 45;
        if (next >= 120) {
          next = 120;
          setAngle(next);
          isPlaying = false;
          playBtn.innerHTML = '↺ Reset';
          playBtn.classList.remove('active');
          return;
        }
        setAngle(next);
        animFrame = requestAnimationFrame(animateLoop);
      }
    }

    playBtn.addEventListener('click', () => {
      if (currentAngle >= 120) {
        setAngle(0);
        isPlaying = true;
        playBtn.innerHTML = '⏸ Pause';
        playBtn.classList.add('active');
        lastTime = null;
        animFrame = requestAnimationFrame(animateLoop);
      } else if (isPlaying) {
        isPlaying = false;
        playBtn.innerHTML = '▶ Rotate';
        playBtn.classList.remove('active');
      } else {
        isPlaying = true;
        playBtn.innerHTML = '⏸ Pause';
        playBtn.classList.add('active');
        lastTime = null;
        animFrame = requestAnimationFrame(animateLoop);
      }
    });

    slider.addEventListener('input', (e) => {
      if (isPlaying) {
        isPlaying = false;
        playBtn.classList.remove('active');
      }
      playBtn.innerHTML = e.target.value >= 120 ? '↺ Reset' : '▶ Rotate';
      setAngle(parseFloat(e.target.value));
    });

    setAngle(0);
  </script>
</body>
</html>

Rigid Plane Motions: Translations, Reflections, and Rotations

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    html, body {
      width: 100%;
      height: 100%;
      background: transparent;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      display: flex;
      align-items: center;
      justify-content: center;
      overflow: hidden;
    }
    .diagram-svg {
      width: 100%;
      max-width: 620px;
      height: auto;
      display: block;
      user-select: none;
    }
    text {
      font-family: inherit;
    }
  </style>
</head>
<body>
  <svg class="diagram-svg" viewBox="0 0 600 320" xmlns="http://www.w3.org/2000/svg">
    <defs>
      
      <marker id="arrow-slate" markerWidth="6" markerHeight="6" refX="5" refY="3" orient="auto">
        <path d="M0,0 L6,3 L0,6 Z" fill="#64748b" />
      </marker>
      <marker id="arrow-green" markerWidth="6" markerHeight="6" refX="5" refY="3" orient="auto">
        <path d="M0,0 L6,3 L0,6 Z" fill="#16a34a" />
      </marker>
      <marker id="arrow-red" markerWidth="6" markerHeight="6" refX="5" refY="3" orient="auto">
        <path d="M0,0 L6,3 L0,6 Z" fill="#dc2626" />
      </marker>

      
      <marker id="dim-tick" markerWidth="2" markerHeight="6" refX="1" refY="3" orient="auto">
        <line x1="1" y1="0" x2="1" y2="6" stroke="#64748b" stroke-width="1.5" />
      </marker>
    </defs>

    
    <line x1="300" y1="18" x2="300" y2="302" stroke="#cbd5e1" stroke-width="1.5" stroke-dasharray="4 4" />

    
    
    <g transform="translate(150, 24)">
      <rect x="-115" y="-14" width="230" height="28" rx="14" fill="#ecfdf5" stroke="#a7f3d0" stroke-width="1" />
      <text x="0" y="4" font-size="13" font-weight="700" fill="#047857" text-anchor="middle">✓ Rigid Motion</text>
    </g>

    
    <g transform="translate(42, 95)">
      <rect x="0" y="0" width="44" height="66" rx="3" fill="#f8fafc" stroke="#64748b" stroke-width="1.8" stroke-dasharray="4 3" />
      
      <text x="22" y="-7" font-size="12" font-weight="600" fill="#64748b" text-anchor="middle">4</text>
      <text x="-9" y="37" font-size="12" font-weight="600" fill="#64748b" text-anchor="middle">6</text>
      <text x="22" y="37" font-size="10" font-weight="500" fill="#94a3b8" text-anchor="middle">Start</text>
    </g>

    
    <path d="M 98,124 Q 138,98 168,118" fill="none" stroke="#16a34a" stroke-width="2" stroke-dasharray="3 2" marker-end="url(#arrow-green)" />
    <text x="135" y="104" font-size="10" font-weight="600" fill="#16a34a" text-anchor="middle">Slide &amp; Turn</text>

    
    <g transform="translate(206, 142) rotate(25)">
      <rect x="-22" y="-33" width="44" height="66" rx="3" fill="#dcfce7" stroke="#16a34a" stroke-width="2" />
      
      <text x="0" y="-39" font-size="12" font-weight="700" fill="#15803d" text-anchor="middle">4</text>
      <text x="-30" y="4" font-size="12" font-weight="700" fill="#15803d" text-anchor="middle">6</text>
    </g>

    
    <g transform="translate(150, 276)">
      <rect x="-105" y="-13" width="210" height="26" rx="6" fill="#f0fdf4" stroke="#86efac" stroke-width="1" />
      <text x="0" y="4" font-size="12" font-weight="600" fill="#15803d" text-anchor="middle">Side lengths preserved: YES</text>
    </g>


    
    
    <g transform="translate(450, 24)">
      <rect x="-115" y="-14" width="230" height="28" rx="14" fill="#fef2f2" stroke="#fecaca" stroke-width="1" />
      <text x="0" y="4" font-size="13" font-weight="700" fill="#b91c1c" text-anchor="middle">✕ Not Rigid (Dilation)</text>
    </g>

    
    <g transform="translate(332, 110)">
      <rect x="0" y="0" width="44" height="66" rx="3" fill="#f8fafc" stroke="#64748b" stroke-width="1.8" stroke-dasharray="4 3" />
      
      <text x="22" y="-7" font-size="12" font-weight="600" fill="#64748b" text-anchor="middle">4</text>
      <text x="-9" y="37" font-size="12" font-weight="600" fill="#64748b" text-anchor="middle">6</text>
      <text x="22" y="37" font-size="10" font-weight="500" fill="#94a3b8" text-anchor="middle">Start</text>
    </g>

    
    <path d="M 388,143 L 424,143" fill="none" stroke="#dc2626" stroke-width="2" marker-end="url(#arrow-red)" />
    <text x="406" y="133" font-size="11" font-weight="700" fill="#dc2626" text-anchor="middle">×2</text>

    
    <g transform="translate(442, 68)">
      <rect x="0" y="0" width="88" height="132" rx="4" fill="#fee2e2" stroke="#dc2626" stroke-width="2" />
      
      <text x="44" y="-8" font-size="13" font-weight="700" fill="#b91c1c" text-anchor="middle">8</text>
      <text x="102" y="71" font-size="13" font-weight="700" fill="#b91c1c" text-anchor="start">12</text>
    </g>

    
    <g transform="translate(450, 276)">
      <rect x="-105" y="-13" width="210" height="26" rx="6" fill="#fef2f2" stroke="#fca5a5" stroke-width="1" />
      <text x="0" y="4" font-size="12" font-weight="600" fill="#b91c1c" text-anchor="middle">Side lengths preserved: NO</text>
    </g>
  </svg>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #ffffff;
      color: #1e293b;
      padding: 8px 6px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: flex-start;
      gap: 8px;
      overflow-x: hidden;
    }

    .grid-container {
      display: grid;
      grid-template-columns: repeat(3, 1fr);
      gap: 6px;
      width: 100%;
      max-width: 620px;
    }

    @media (max-width: 480px) {
      .grid-container {
        grid-template-columns: 1fr;
        gap: 8px;
      }
    }

    .motion-card {
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      padding: 6px 4px 4px;
      display: flex;
      flex-direction: column;
      align-items: center;
    }

    .card-title {
      font-size: 12px;
      font-weight: 700;
      letter-spacing: 0.2px;
      color: #334155;
      margin-bottom: 2px;
    }

    svg {
      width: 100%;
      height: auto;
      max-height: 145px;
      overflow: visible;
      display: block;
    }

    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      width: 100%;
      max-width: 400px;
      padding: 5px 12px;
      background: #f1f5f9;
      border-radius: 16px;
    }

    .btn {
      background: #0ea5e9;
      color: white;
      border: none;
      border-radius: 12px;
      padding: 4px 12px;
      font-size: 12px;
      font-weight: 600;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      justify-content: center;
      min-width: 65px;
      user-select: none;
      transition: background 0.15s ease, opacity 0.15s ease;
    }
    .btn:hover { background: #0284c7; }
    .btn:active { opacity: 0.85; }

    .slider {
      flex: 1;
      accent-color: #6366f1;
      cursor: pointer;
      height: 5px;
    }

    /* SVG typography & styling */
    .lbl {
      font-size: 10px;
      font-weight: 700;
      font-family: inherit;
    }
    .lbl-pre { fill: #0284c7; }
    .lbl-img { fill: #4f46e5; }
    .lbl-aux { fill: #64748b; font-size: 9px; font-weight: 600; }
  </style>
</head>
<body>

  <div class="grid-container">
    
    <div class="motion-card">
      <div class="card-title">1. Translation (Slide)</div>
      <svg viewBox="0 0 170 140" id="svg-trans">
        <defs>
          <marker id="arrow-t" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="5" markerHeight="5" orient="auto-start-reverse">
            <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#94a3b8" />
          </marker>
        </defs>

        
        <path d="M 45 100 L 115 50" stroke="#cbd5e1" stroke-width="1.5" stroke-dasharray="3 3" marker-end="url(#arrow-t)" />

        
        <polygon points="90,75 135,75 105,25" fill="#6366f1" fill-opacity="0.12" stroke="#6366f1" stroke-width="1.5" stroke-dasharray="3 2" />
        <line x1="112.5" y1="72" x2="112.5" y2="78" stroke="#818cf8" stroke-width="1.2" />
        <line x1="96" y1="49" x2="101" y2="51" stroke="#818cf8" stroke-width="1.2" />
        <line x1="97" y1="46" x2="102" y2="48" stroke="#818cf8" stroke-width="1.2" />
        <text x="80" y="82" class="lbl lbl-img">A'</text>
        <text x="138" y="82" class="lbl lbl-img">B'</text>
        <text x="101" y="18" class="lbl lbl-img">C'</text>

        
        <polygon points="20,125 65,125 35,75" fill="#0ea5e9" fill-opacity="0.3" stroke="#0ea5e9" stroke-width="1.8" />
        
        <line x1="42.5" y1="122" x2="42.5" y2="128" stroke="#0284c7" stroke-width="1.5" />
        <line x1="26" y1="99" x2="31" y2="101" stroke="#0284c7" stroke-width="1.5" />
        <line x1="27" y1="96" x2="32" y2="98" stroke="#0284c7" stroke-width="1.5" />
        <text x="10" y="132" class="lbl lbl-pre">A</text>
        <text x="68" y="132" class="lbl lbl-pre">B</text>
        <text x="31" y="68" class="lbl lbl-pre">C</text>

        
        <g id="trans-group" opacity="0">
          <polygon points="20,125 65,125 35,75" fill="#6366f1" fill-opacity="0.65" stroke="#4f46e5" stroke-width="2" />
          <line x1="42.5" y1="122" x2="42.5" y2="128" stroke="#ffffff" stroke-width="1.5" />
          <line x1="26" y1="99" x2="31" y2="101" stroke="#ffffff" stroke-width="1.5" />
          <line x1="27" y1="96" x2="32" y2="98" stroke="#ffffff" stroke-width="1.5" />
        </g>
      </svg>
    </div>

    
    <div class="motion-card">
      <div class="card-title">2. Reflection (Flip)</div>
      <svg viewBox="0 0 170 140" id="svg-refl">
        
        <line x1="85" y1="12" x2="85" y2="135" stroke="#94a3b8" stroke-width="1.5" stroke-dasharray="4 3" />
        <text x="89" y="20" class="lbl lbl-aux">Mirror</text>

        
        <polygon points="145,125 105,125 145,65" fill="#6366f1" fill-opacity="0.12" stroke="#6366f1" stroke-width="1.5" stroke-dasharray="3 2" />
        <line x1="125" y1="122" x2="125" y2="128" stroke="#818cf8" stroke-width="1.2" />
        <line x1="142" y1="95" x2="148" y2="95" stroke="#818cf8" stroke-width="1.2" />
        <line x1="142" y1="92" x2="148" y2="92" stroke="#818cf8" stroke-width="1.2" />
        <text x="148" y="132" class="lbl lbl-img">A'</text>
        <text x="92" y="132" class="lbl lbl-img">B'</text>
        <text x="148" y="60" class="lbl lbl-img">C'</text>

        
        <polygon points="25,125 65,125 25,65" fill="#0ea5e9" fill-opacity="0.3" stroke="#0ea5e9" stroke-width="1.8" />
        
        <line x1="45" y1="122" x2="45" y2="128" stroke="#0284c7" stroke-width="1.5" />
        <line x1="22" y1="95" x2="28" y2="95" stroke="#0284c7" stroke-width="1.5" />
        <line x1="22" y1="92" x2="28" y2="92" stroke="#0284c7" stroke-width="1.5" />
        <text x="14" y="132" class="lbl lbl-pre">A</text>
        <text x="68" y="132" class="lbl lbl-pre">B</text>
        <text x="14" y="60" class="lbl lbl-pre">C</text>

        
        <g id="refl-group" opacity="0">
          <polygon points="25,125 65,125 25,65" fill="#6366f1" fill-opacity="0.65" stroke="#4f46e5" stroke-width="2" />
          <line x1="45" y1="122" x2="45" y2="128" stroke="#ffffff" stroke-width="1.5" />
          <line x1="22" y1="95" x2="28" y2="95" stroke="#ffffff" stroke-width="1.5" />
          <line x1="22" y1="92" x2="28" y2="92" stroke="#ffffff" stroke-width="1.5" />
        </g>
      </svg>
    </div>

    
    <div class="motion-card">
      <div class="card-title">3. Rotation (90° Turn)</div>
      <svg viewBox="0 0 170 140" id="svg-rot">
        <defs>
          <marker id="arrow-r" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="5" markerHeight="5" orient="auto-start-reverse">
            <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#94a3b8" />
          </marker>
        </defs>

        
        <circle cx="85" cy="110" r="3.5" fill="#334155" />
        <text x="85" y="125" class="lbl" fill="#334155" text-anchor="middle">P (Center)</text>

        
        <path d="M 25 55 A 81.4 81.4 0 0 1 140 50" fill="none" stroke="#cbd5e1" stroke-width="1.5" stroke-dasharray="3 3" marker-end="url(#arrow-r)" />

        
        <polygon points="140,50 140,85 105,50" fill="#6366f1" fill-opacity="0.12" stroke="#6366f1" stroke-width="1.5" stroke-dasharray="3 2" />
        <line x1="137" y1="67.5" x2="143" y2="67.5" stroke="#818cf8" stroke-width="1.2" />
        <line x1="121" y1="47" x2="121" y2="53" stroke="#818cf8" stroke-width="1.2" />
        <line x1="124" y1="47" x2="124" y2="53" stroke="#818cf8" stroke-width="1.2" />
        <text x="145" y="48" class="lbl lbl-img">A'</text>
        <text x="145" y="90" class="lbl lbl-img">B'</text>
        <text x="96" y="44" class="lbl lbl-img">C'</text>

        
        <polygon points="25,55 60,55 25,90" fill="#0ea5e9" fill-opacity="0.3" stroke="#0ea5e9" stroke-width="1.8" />
        
        <line x1="42.5" y1="52" x2="42.5" y2="58" stroke="#0284c7" stroke-width="1.5" />
        <line x1="22" y1="71" x2="28" y2="71" stroke="#0284c7" stroke-width="1.5" />
        <line x1="22" y1="74" x2="28" y2="74" stroke="#0284c7" stroke-width="1.5" />
        <text x="14" y="54" class="lbl lbl-pre">A</text>
        <text x="58" y="44" class="lbl lbl-pre">B</text>
        <text x="14" y="98" class="lbl lbl-pre">C</text>

        
        <g id="rot-group" opacity="0">
          <polygon points="25,55 60,55 25,90" fill="#6366f1" fill-opacity="0.65" stroke="#4f46e5" stroke-width="2" />
          <line x1="42.5" y1="52" x2="42.5" y2="58" stroke="#ffffff" stroke-width="1.5" />
          <line x1="22" y1="71" x2="28" y2="71" stroke="#ffffff" stroke-width="1.5" />
          <line x1="22" y1="74" x2="28" y2="74" stroke="#ffffff" stroke-width="1.5" />
        </g>
      </svg>
    </div>
  </div>

  
  <div class="controls">
    <button id="playBtn" class="btn">▶ Play</button>
    <input id="scrubber" type="range" class="slider" min="0" max="1" step="0.005" value="0" aria-label="Animation progress">
  </div>

  <script>
    const scrubber = document.getElementById('scrubber');
    const playBtn = document.getElementById('playBtn');

    const transG = document.getElementById('trans-group');
    const reflG = document.getElementById('refl-group');
    const rotG = document.getElementById('rot-group');

    let progress = 0;
    let isPlaying = false;
    let animId = null;

    function applyProgress(t) {
      // Dynamic opacity: 0 at rest (t=0), full when animated
      const activeOpacity = t === 0 ? 0 : Math.min(1, t * 4 + 0.3);

      // 1. Translation: slide along dx=70, dy=-50
      const dx = 70 * t;
      const dy = -50 * t;
      transG.setAttribute('transform', `translate(${dx}, ${dy})`);
      transG.setAttribute('opacity', activeOpacity);

      // 2. Reflection: fold/flip across x = 85
      const scaleX = 1 - 2 * t;
      reflG.setAttribute('transform', `translate(85, 0) scale(${scaleX}, 1) translate(-85, 0)`);
      reflG.setAttribute('opacity', activeOpacity);

      // 3. Rotation: turn 90° CW around P(85, 110)
      const angle = 90 * t;
      rotG.setAttribute('transform', `rotate(${angle}, 85, 110)`);
      rotG.setAttribute('opacity', activeOpacity);
    }

    function render() {
      applyProgress(progress);
      scrubber.value = progress;
    }

    let lastTime = null;
    function loop(time) {
      if (!lastTime) lastTime = time;
      const delta = (time - lastTime) / 1000;
      lastTime = time;

      if (isPlaying) {
        progress += delta * 0.45; // ~2.2s complete cycle
        if (progress >= 1) {
          progress = 1;
          render();
          isPlaying = false;
          playBtn.textContent = '↺ Reset';
          return;
        }
        render();
        animId = requestAnimationFrame(loop);
      }
    }

    playBtn.addEventListener('click', () => {
      if (progress >= 1) {
        progress = 0;
        render();
        isPlaying = true;
        playBtn.textContent = '⏸ Pause';
        lastTime = null;
        animId = requestAnimationFrame(loop);
      } else if (isPlaying) {
        isPlaying = false;
        playBtn.textContent = '▶ Play';
        cancelAnimationFrame(animId);
      } else {
        isPlaying = true;
        playBtn.textContent = '⏸ Pause';
        lastTime = null;
        animId = requestAnimationFrame(loop);
      }
    });

    scrubber.addEventListener('input', (e) => {
      if (isPlaying) {
        isPlaying = false;
        cancelAnimationFrame(animId);
      }
      progress = parseFloat(e.target.value);
      playBtn.textContent = progress >= 1 ? '↺ Reset' : '▶ Play';
      render();
    });

    // Initial render at rest (t = 0)
    render();
  </script>
</body>
</html>

生活中的对称现象与轴对称的概念

轴对称图形与两个图形成轴对称的区别与联系

轴对称的性质：对应点连线被对称轴垂直平分

轴对称中对应线段相等与对应角相等

根据成轴对称的两个图形确定对称轴

自然界中的轴对称：动植物与晶体构造

人文建筑与艺术设计中的轴对称

标志、车标与徽标中的轴对称分析

用折纸实验探究多条对称轴的图形

轴对称与轴对称图形的辨析与综合反思

math

图形的轴对称：概念、性质与生活中的对称

作一个点关于已知直线的对称点

作线段关于直线的对称线段

作三角形关于直线的对称三角形

作多边形关于任意斜直线的对称图形

直角坐标系中关于 x 轴对称的点的坐标特征

直角坐标系中关于 y 轴对称的点的坐标特征

关于平行于坐标轴的直线对称的坐标推算

在直角坐标系中利用坐标画轴对称图形

将军饮马问题与轴对称求线段和最值

轴对称作图的规范性与综合应用

轴对称作图与直角坐标系中的轴对称

Side-Side-Side (SSS) Triangle Congruence

Side-Angle-Side (SAS) Triangle Congruence

Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS) Congruence

Hypotenuse-Leg (HL) Congruence for Right Triangles

Why AAA and SSA Do Not Guarantee Triangle Congruence

Writing Two-Column and Paragraph Proofs for Congruent Triangles

Triangle Congruence Criteria and Proofs

等腰三角形的轴对称性与三线合一

等边三角形的三条对称轴与中心特征

矩形的两条对称轴与垂直平分线特征

菱形的对称轴与对角线所在直线

正方形的四条对称轴与综合对称性

正多边形的边数与对称轴条数的规律

圆的无限条对称轴与垂径定理的本质

等腰梯形的轴对称性与性质探究

常见平面几何图形对称轴条数大比拼

利用图形的轴对称性质进行几何证明与计算

常见几何图形的轴对称性质深化

Visual and Algebraic Proofs of the Pythagorean Theorem

Deriving the Pythagorean Theorem Using Similar Triangles

Calculating the Hypotenuse of a Right Triangle

Calculating an Unknown Leg of a Right Triangle

Identifying Pythagorean Triples

Classifying Acute, Right, and Obtuse Triangles Using Side Lengths

Finding Distances on the Coordinate Plane Using Pythagoras

Calculating Perimeter and Area of Composite Right Triangles

Solving 3D Pythagorean Problems in Boxes and Cones

The Pythagorean Theorem and Right Triangle Geometry

生活中的平移现象与平移的数学定义

平移的性质：对应点连线平行（或共线）且相等

平移前后图形形状、大小及对应角的关系

按指定方向和距离作三角形的平移图形

直角坐标系中点的左右平移与横坐标变化

直角坐标系中点的上下平移与纵坐标变化

平面直角坐标系中图形的两次连续平移（斜向平移）

工程建筑、传送带与现代交通中的平移应用

利用平移转化法求不规则图形的周长与面积

平移在平行线性质与几何证明中的应用

图形的平移：概念、性质与坐标变换

生活中的旋转现象与旋转的三要素

旋转的基本性质：对应点到中心距离相等与旋转角相等

旋转变换中图形的全等性与对应线段角关系

作一个点绕旋转中心旋转给定角度后的点

作线段与三角形绕定点旋转后的图形

旋转构造中的等腰三角形模型与角平分线

共顶点等边三角形（或等腰直角三角形）的旋转与手拉手模型

直角坐标系中点绕原点顺时针与逆时针旋转 90° 的坐标规律

旋转中的动点轨迹与线段最值探究

旋转性质在综合几何证明中的转化策略

图形的旋转：概念、旋转三要素与性质

中心对称的概念：旋转 180° 的特殊旋转变换

中心对称的性质：对应点连线经过对称中心且被其平分

中心对称图形的概念与判定方法

作点、线段和三角形关于定点的中心对称图形

线段与平行四边形的中心对称性探索

正多边形的中心对称性：偶数边正多边形的对称中心

圆的中心对称性与圆心特征

直角坐标系中关于原点对称的点的坐标变化

自然界与生活中的中心对称图形欣赏与应用

轴对称图形与中心对称图形的综合对比与辨析

中心对称与中心对称图形

平移、旋转与轴对称的共性（全等变换）与特征对比

图形的连续变换：平移与轴对称的复合

运用轴对称进行剪纸与徽章图案设计

运用平移设计花边与连续二方连续纹样

运用旋转设计万花筒与旋转对称艺术图案

平面镶嵌原理：用单一种类或多种正多边形密铺平面

埃舍尔式图形变换与创意平面密铺设计

直角坐标系中图形运动的代数表达综合

图案设计成果展评与背后的几何变换原理解析

全等变换单元思维导图与方法归纳

图形变换的综合应用与平面图案设计

Translations on the Coordinate Plane Using Vectors and Rules

Reflections Across Axes and Arbitrary Lines

Rotations Around the Origin and Given Points

Translations, Reflections, and Rotations on the Coordinate Plane

Identifying All Lines of Symmetry in Triangles and Quadrilaterals

Line Symmetry, Rotational Symmetry, and Point Symmetry

Rigid Transformations and Symmetry in the Plane

Dilations with Centers Not at the Origin

Identifying Similar Figures Using Transformations

Angle-Angle (AA) Similarity Criterion for Triangles

SAS and SSS Similarity Criteria for Triangles

Solving Problems with Similar Triangles

Perimeters and Areas of Similar Triangles

Areas and Volumes of Similar Figures

Scale Drawings, Maps, and Indirect Measurement Applications

Dilations, Similarity, and Scale Drawings

Concepto de razón y formas de representación

Razones equivalentes y tablas de razón

Concepto de tasa y tasa unitaria

Comparación de precios unitarios para la mejor compra

Concepto de proporcionalidad directa y constante k

Ecuaciones de proporcionalidad directa: y = kx

Gráficas de proporcionalidad directa en el plano

Regla de tres simple directa

Problemas de velocidad constante, distancia y tiempo

Factores de conversión unitarios con proporcionalidad

Razones, tasas y proporcionalidad directa

相似三角形性质：对应高的比等于相似比

相似三角形性质：对应中线与对应角平分线的比等于相似比

相似三角形周长比等于相似比的严密证明与应用

相似三角形面积比等于相似比的平方的严密证明与计算

双垂直（母子三角形）模型与射影定理推导

一线三等角（K 字型）相似模型解析与应用

旋转相似与大小手拉手几何模型

相似三角形中的辅助线构造：做平行线与截长补短

相似三角形在圆中的应用：相交弦与切割线性质

相似三角形性质的综合几何代数化求解

相似三角形的性质定理与经典几何模型

Concepto de proporcionalidad inversa

Tablas y gráficas de proporcionalidad inversa

Regla de tres simple inversa

Comparación entre proporcionalidad directa e inversa

Concepto de porcentaje y equivalencias fracción-decimal

Cálculo del porcentaje de una cantidad

Hallar la cantidad total a partir de un porcentaje

Porcentaje de aumento y descuento comercial

Cálculo de impuestos (IVA) y propinas

Interés simple: fórmula y aplicaciones

Variación porcentual: incremento y decremento

Proporcionalidad inversa, porcentajes y finanzas

Estructura del plano cartesiano: cuadrantes y ejes

Localización y graficación de puntos con coordenadas enteras

Puntos con coordenadas fraccionarias y decimales en el plano

Distancia entre puntos horizontales y verticales en el plano

Figuras geométricas y polígonos en el plano cartesiano

Variables independientes y dependientes en tablas

Graficación de relaciones lineales a partir de ecuaciones

Interpretación de gráficas de dos variables en contextos reales

Sistemas de coordenadas geográficas: latitud y longitud

El plano cartesiano y relaciones lineales

解直角三角形的概念与边角五元素关系

基本类型一：已知两边（两直角边或一直角边一斜边）解直角三角形

基本类型二：已知一边一锐角解直角三角形

仰角与俯角问题：测量建筑物与无人机高度

方向角（方位角）问题：航海避礁与航空飞行定位

坡度与坡角问题：堤坝防洪与公路铁路工程坡比计算

化一般三角形为直角三角形：作高线（分割或补形）解题策略

OGM.8.GEO.7

Aligned learning resources

Related diagrams