<!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;
      -webkit-tap-highlight-color: transparent;
    }

    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background-color: #f8f9fa;
      color: #1e2945;
      min-height: 100%;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      padding: 16px 12px;
      user-select: none;
    }

    .decoder-wrap {
      width: 100%;
      max-width: 540px;
      display: flex;
      flex-direction: column;
      gap: 16px;
    }

    /* Top Statement Display */
    .statement-box {
      background: #ffffff;
      border: 1.5px solid #e2e8f0;
      border-radius: 12px;
      padding: 16px 12px;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      font-size: 22px;
      font-weight: 700;
      box-shadow: 0 2px 6px rgba(0, 0, 0, 0.03);
    }

    .tri-group {
      display: inline-flex;
      align-items: center;
      gap: 4px;
    }

    .sym {
      color: #64748b;
      font-weight: 600;
      padding: 0 4px;
    }

    .cong-sym {
      color: #1e2945;
      font-size: 24px;
      padding: 0 6px;
    }

    /* Color Coded Letter Badges */
    .letter {
      display: inline-flex;
      align-items: center;
      justify-content: center;
      width: 32px;
      height: 36px;
      border-radius: 6px;
      border: 2px solid transparent;
      transition: background-color 0.2s ease, box-shadow 0.2s ease, border-color 0.2s ease, opacity 0.2s ease;
      cursor: pointer;
    }

    .letter-a, .letter-d {
      color: #dc2626;
      background: #fee2e2;
    }
    .letter-b, .letter-e {
      color: #16a34a;
      background: #dcfce7;
    }
    .letter-c, .letter-f {
      color: #7c3aed;
      background: #f3e8ff;
    }

    .letter.dimmed {
      opacity: 0.28;
    }

    .letter.active {
      opacity: 1;
      border-color: currentColor;
      box-shadow: 0 0 0 3px rgba(0, 0, 0, 0.08);
    }

    /* Columns Layout */
    .columns-grid {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 12px;
    }

    .col-card {
      background: #ffffff;
      border: 1.5px solid #e2e8f0;
      border-radius: 12px;
      padding: 12px;
      display: flex;
      flex-direction: column;
      gap: 8px;
    }

    .col-title {
      font-size: 13px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      color: #64748b;
      text-align: center;
      padding-bottom: 4px;
      border-bottom: 1px solid #f1f5f9;
    }

    .pair-btn {
      background: #f8fafc;
      border: 1.5px solid #e2e8f0;
      border-radius: 8px;
      padding: 8px 10px;
      font-size: 16px;
      font-weight: 600;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      cursor: pointer;
      transition: background-color 0.2s ease, border-color 0.2s ease, box-shadow 0.2s ease, opacity 0.2s ease;
    }

    .pair-btn.dimmed {
      opacity: 0.35;
    }

    .pair-btn.active {
      opacity: 1;
      background: #ffffff;
      border-color: #22b7ff;
      box-shadow: 0 0 0 2px rgba(34, 183, 255, 0.25);
    }

    /* Segment Overline */
    .seg {
      text-decoration: overline;
      text-decoration-thickness: 1.5px;
      display: inline-flex;
    }

    .pair-cong {
      color: #94a3b8;
      font-size: 15px;
      font-weight: 400;
    }

    .badge-a, .badge-d { color: #dc2626; }
    .badge-b, .badge-e { color: #16a34a; }
    .badge-c, .badge-f { color: #7c3aed; }

    @media (max-width: 400px) {
      .statement-box {
        font-size: 19px;
        gap: 4px;
        padding: 12px 8px;
      }
      .letter {
        width: 28px;
        height: 32px;
      }
      .cong-sym {
        font-size: 20px;
        padding: 0 3px;
      }
      .pair-btn {
        font-size: 14px;
        padding: 7px 6px;
        gap: 6px;
      }
      .col-title {
        font-size: 11px;
      }
    }
  </style>
</head>
<body>

  <div class="decoder-wrap">
    
    <div class="statement-box" id="statementBox">
      <div class="tri-group">
        <span class="sym">△</span>
        <span class="letter letter-a" id="let-a">A</span>
        <span class="letter letter-b" id="let-b">B</span>
        <span class="letter letter-c" id="let-c">C</span>
      </div>
      <span class="cong-sym">≅</span>
      <div class="tri-group">
        <span class="sym">△</span>
        <span class="letter letter-d" id="let-d">D</span>
        <span class="letter letter-e" id="let-e">E</span>
        <span class="letter letter-f" id="let-f">F</span>
      </div>
    </div>

    
    <div class="columns-grid">
      
      <div class="col-card">
        <div class="col-title">Corresponding Angles</div>

        <div class="pair-btn" data-targets="a,d">
          <span>∠<span class="badge-a">A</span></span>
          <span class="pair-cong">≅</span>
          <span>∠<span class="badge-d">D</span></span>
        </div>

        <div class="pair-btn" data-targets="b,e">
          <span>∠<span class="badge-b">B</span></span>
          <span class="pair-cong">≅</span>
          <span>∠<span class="badge-e">E</span></span>
        </div>

        <div class="pair-btn" data-targets="c,f">
          <span>∠<span class="badge-c">C</span></span>
          <span class="pair-cong">≅</span>
          <span>∠<span class="badge-f">F</span></span>
        </div>
      </div>

      
      <div class="col-card">
        <div class="col-title">Corresponding Sides</div>

        <div class="pair-btn" data-targets="a,b,d,e">
          <span class="seg"><span class="badge-a">A</span><span class="badge-b">B</span></span>
          <span class="pair-cong">≅</span>
          <span class="seg"><span class="badge-d">D</span><span class="badge-e">E</span></span>
        </div>

        <div class="pair-btn" data-targets="b,c,e,f">
          <span class="seg"><span class="badge-b">B</span><span class="badge-c">C</span></span>
          <span class="pair-cong">≅</span>
          <span class="seg"><span class="badge-e">E</span><span class="badge-f">F</span></span>
        </div>

        <div class="pair-btn" data-targets="a,c,d,f">
          <span class="seg"><span class="badge-a">A</span><span class="badge-c">C</span></span>
          <span class="pair-cong">≅</span>
          <span class="seg"><span class="badge-d">D</span><span class="badge-f">F</span></span>
        </div>
      </div>
    </div>
  </div>

  <script>
    const letters = {
      a: document.getElementById('let-a'),
      b: document.getElementById('let-b'),
      c: document.getElementById('let-c'),
      d: document.getElementById('let-d'),
      e: document.getElementById('let-e'),
      f: document.getElementById('let-f')
    };

    const pairButtons = document.querySelectorAll('.pair-btn');
    let lockedTargets = null;

    function applyHighlight(targetKeys) {
      if (!targetKeys) {
        Object.values(letters).forEach(el => {
          el.classList.remove('active', 'dimmed');
        });
        pairButtons.forEach(btn => btn.classList.remove('active', 'dimmed'));
        return;
      }

      const activeSet = new Set(targetKeys);

      Object.entries(letters).forEach(([k, el]) => {
        if (activeSet.has(k)) {
          el.classList.add('active');
          el.classList.remove('dimmed');
        } else {
          el.classList.remove('active');
          el.classList.add('dimmed');
        }
      });

      pairButtons.forEach(btn => {
        const btnTargets = btn.getAttribute('data-targets').split(',');
        const isMatch = btnTargets.length === targetKeys.length && btnTargets.every(t => activeSet.has(t));
        if (isMatch) {
          btn.classList.add('active');
          btn.classList.remove('dimmed');
        } else {
          btn.classList.remove('active');
          btn.classList.add('dimmed');
        }
      });
    }

    pairButtons.forEach(btn => {
      const targets = btn.getAttribute('data-targets').split(',');

      btn.addEventListener('mouseenter', () => {
        if (!lockedTargets) applyHighlight(targets);
      });

      btn.addEventListener('mouseleave', () => {
        if (!lockedTargets) applyHighlight(null);
      });

      btn.addEventListener('click', (e) => {
        e.stopPropagation();
        const currentKey = targets.join(',');
        if (lockedTargets === currentKey) {
          lockedTargets = null;
          applyHighlight(null);
        } else {
          lockedTargets = currentKey;
          applyHighlight(targets);
        }
      });
    });

    // Tap letters directly to decode corresponding angle
    const letterMap = { a: ['a','d'], d: ['a','d'], b: ['b','e'], e: ['b','e'], c: ['c','f'], f: ['c','f'] };
    Object.entries(letters).forEach(([k, el]) => {
      el.addEventListener('mouseenter', () => {
        if (!lockedTargets) applyHighlight(letterMap[k]);
      });
      el.addEventListener('mouseleave', () => {
        if (!lockedTargets) applyHighlight(null);
      });
      el.addEventListener('click', (e) => {
        e.stopPropagation();
        const currentKey = letterMap[k].join(',');
        if (lockedTargets === currentKey) {
          lockedTargets = null;
          applyHighlight(null);
        } else {
          lockedTargets = currentKey;
          applyHighlight(letterMap[k]);
        }
      });
    });

    document.body.addEventListener('click', () => {
      lockedTargets = null;
      applyHighlight(null);
    });
  </script>
</body>
</html>

Concept of Geometric Congruence and Rigid Motions

<!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">
  <link rel="stylesheet" href="{{VENDOR_CDN}}/katex.min.css">
  <script src="{{VENDOR_CDN}}/katex.min.js"></script>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }
    body {
      background: #ffffff;
      color: #1e2945;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 12px;
      gap: 10px;
    }

    .header-badge {
      display: inline-flex;
      align-items: center;
      gap: 6px;
      background: #f1f5f9;
      border: 1px solid #e2e8f0;
      padding: 4px 12px;
      border-radius: 999px;
      font-size: 13px;
      font-weight: 700;
      color: #1e2945;
    }

    .main-stage {
      display: flex;
      flex-direction: row;
      flex-wrap: wrap;
      align-items: center;
      justify-content: center;
      gap: 16px;
      width: 100%;
      max-width: 620px;
    }

    .svg-container {
      flex: 1 1 290px;
      max-width: 320px;
      background: #fafbfd;
      border: 1px solid #e6e6e6;
      border-radius: 12px;
      padding: 8px;
      display: flex;
      align-items: center;
      justify-content: center;
    }

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

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

    .eq-card {
      border: 1px solid #e6e6e6;
      background: #ffffff;
      border-radius: 10px;
      padding: 10px 12px;
      transition: border-color 0.25s ease, background-color 0.25s ease, box-shadow 0.25s ease;
      cursor: pointer;
    }

    .eq-card.active-blue {
      border-color: #0284c7;
      background: #f0f9ff;
      box-shadow: 0 2px 8px rgba(2, 132, 199, 0.12);
    }

    .eq-card.active-orange {
      border-color: #ea580c;
      background: #fff7ed;
      box-shadow: 0 2px 8px rgba(234, 88, 12, 0.12);
    }

    .eq-header {
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      margin-bottom: 4px;
      display: flex;
      align-items: center;
      gap: 6px;
    }

    .eq-header.blue { color: #0284c7; }
    .eq-header.orange { color: #ea580c; }

    .math-row {
      font-size: 15px;
      line-height: 1.4;
      color: #1e2945;
      min-height: 24px;
    }

    .controls {
      display: flex;
      gap: 8px;
      width: 100%;
      max-width: 440px;
      justify-content: center;
    }

    .btn-tab {
      flex: 1;
      padding: 8px 12px;
      font-size: 13px;
      font-weight: 600;
      border: 1px solid #e2e8f0;
      background: #ffffff;
      color: #475569;
      border-radius: 8px;
      cursor: pointer;
      transition: all 0.2s ease;
      text-align: center;
    }

    .btn-tab:hover {
      background: #f8fafc;
      color: #1e2945;
    }

    .btn-tab.active {
      background: #1e2945;
      color: #ffffff;
      border-color: #1e2945;
    }

    /* SVG Elements Styling */
    .triangle-poly {
      fill: #f8fafc;
      stroke: #94a3b8;
      stroke-width: 2;
      stroke-linejoin: round;
    }

    .side-hl {
      stroke: #0284c7;
      stroke-width: 4.5;
      stroke-linecap: round;
      filter: drop-shadow(0 0 3px rgba(2, 132, 199, 0.5));
      transition: opacity 0.3s ease;
    }

    .angle-arc {
      fill: rgba(249, 115, 22, 0.22);
      stroke: #ea580c;
      stroke-width: 2;
      filter: drop-shadow(0 0 4px rgba(234, 88, 12, 0.6));
      transition: opacity 0.3s ease;
    }

    .v-label {
      font-size: 13px;
      font-weight: 700;
      fill: #1e2945;
    }

    .s-label {
      font-size: 12px;
      font-weight: 700;
      fill: #0369a1;
    }

    .a-label {
      font-size: 11.5px;
      font-weight: 700;
      fill: #c2410c;
    }

    .t-title {
      font-size: 12px;
      font-weight: 700;
      fill: #64748b;
    }
  </style>
</head>
<body>

  <div class="header-badge">
    <span>△PQR ≅ △WXY</span>
  </div>

  <div class="main-stage">
    
    <div class="svg-container">
      <svg viewBox="0 0 320 180" aria-label="Congruent Triangles PQR and WXY">
        
        <g id="triPQR">
          <text x="75" y="16" text-anchor="middle" class="t-title">△PQR</text>
          <polygon points="38,32 38,146 138,146" class="triangle-poly" />
          
          
          <line id="hl-pq" x1="38" y1="32" x2="38" y2="146" class="side-hl" />
          
          
          <path id="hl-r" d="M 112,146 A 26,26 0 0 1 120,126 L 138,146 Z" class="angle-arc" />

          
          <text x="32" y="26" text-anchor="end" class="v-label">P</text>
          <text x="28" y="152" text-anchor="end" class="v-label">Q</text>
          <text x="146" y="152" text-anchor="start" class="v-label">R</text>

          
          <text x="28" y="92" text-anchor="end" class="s-label">3x − 5</text>
          
          <text x="110" y="138" text-anchor="middle" class="a-label">?</text>
        </g>

        
        <g id="triWXY">
          <text x="235" y="16" text-anchor="middle" class="t-title">△WXY</text>
          <polygon points="198,32 198,146 298,146" class="triangle-poly" />
          
          
          <line id="hl-wx" x1="198" y1="32" x2="198" y2="146" class="side-hl" />
          
          
          <path id="hl-y" d="M 272,146 A 26,26 0 0 1 280,126 L 298,146 Z" class="angle-arc" />

          
          <text x="192" y="26" text-anchor="end" class="v-label">W</text>
          <text x="188" y="152" text-anchor="end" class="v-label">X</text>
          <text x="306" y="152" text-anchor="start" class="v-label">Y</text>

          
          <text x="188" y="92" text-anchor="end" class="s-label">16</text>
          
          <text x="268" y="138" text-anchor="middle" class="a-label">42°</text>
        </g>
      </svg>
    </div>

    
    <div class="eq-panel">
      
      <div id="card-sides" class="eq-card active-blue" onclick="setMode('sides')">
        <div class="eq-header blue">
          <span>Corresponding Sides</span>
        </div>
        <div class="math-row" id="math-sides"></div>
      </div>

      
      <div id="card-angles" class="eq-card" onclick="setMode('angles')">
        <div class="eq-header orange">
          <span>Corresponding Angles</span>
        </div>
        <div class="math-row" id="math-angles"></div>
      </div>
    </div>
  </div>

  
  <div class="controls">
    <button id="btn-sides" class="btn-tab active" onclick="setMode('sides')">Side PQ = WX</button>
    <button id="btn-angles" class="btn-tab" onclick="setMode('angles')">∠R = ∠Y</button>
    <button id="btn-all" class="btn-tab" onclick="setMode('all')">Both Parts</button>
  </div>

  <script>
    // KaTeX Render
    function renderMath() {
      if (window.katex) {
        katex.render("3x - 5 = 16 \\implies x = 7", document.getElementById('math-sides'), { displayMode: false });
        katex.render("m\\angle R = m\\angle Y = 42^\\circ", document.getElementById('math-angles'), { displayMode: false });
      } else {
        document.getElementById('math-sides').innerText = "3x - 5 = 16 ➔ x = 7";
        document.getElementById('math-angles').innerText = "m∠R = m∠Y = 42°";
      }
    }

    window.addEventListener('DOMContentLoaded', renderMath);
    setTimeout(renderMath, 100);

    const hlPQ = document.getElementById('hl-pq');
    const hlWX = document.getElementById('hl-wx');
    const hlR = document.getElementById('hl-r');
    const hlY = document.getElementById('hl-y');
    const cardSides = document.getElementById('card-sides');
    const cardAngles = document.getElementById('card-angles');
    const btnSides = document.getElementById('btn-sides');
    const btnAngles = document.getElementById('btn-angles');
    const btnAll = document.getElementById('btn-all');

    function setMode(mode) {
      // Buttons state
      btnSides.classList.toggle('active', mode === 'sides');
      btnAngles.classList.toggle('active', mode === 'angles');
      btnAll.classList.toggle('active', mode === 'all');

      if (mode === 'sides') {
        hlPQ.style.opacity = '1';
        hlWX.style.opacity = '1';
        hlR.style.opacity = '0.15';
        hlY.style.opacity = '0.15';

        cardSides.className = 'eq-card active-blue';
        cardAngles.className = 'eq-card';
      } else if (mode === 'angles') {
        hlPQ.style.opacity = '0.15';
        hlWX.style.opacity = '0.15';
        hlR.style.opacity = '1';
        hlY.style.opacity = '1';

        cardSides.className = 'eq-card';
        cardAngles.className = 'eq-card active-orange';
      } else {
        // all
        hlPQ.style.opacity = '1';
        hlWX.style.opacity = '1';
        hlR.style.opacity = '1';
        hlY.style.opacity = '1';

        cardSides.className = 'eq-card active-blue';
        cardAngles.className = 'eq-card active-orange';
      }
    }
  </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="4:3">
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: transparent;
      color: #1e2945;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
    }
    .diagram-grid {
      display: grid;
      grid-template-columns: repeat(3, 1fr);
      gap: 12px;
      width: 100%;
      max-width: 680px;
    }
    .panel {
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      padding: 8px 6px 4px 6px;
      display: flex;
      flex-direction: column;
      align-items: center;
    }
    .panel-title {
      font-size: 13px;
      font-weight: 700;
      color: #1e2945;
      margin-bottom: 2px;
      text-align: center;
    }
    .panel-subtitle {
      font-size: 11px;
      font-weight: 500;
      color: #64748b;
      margin-bottom: 4px;
      text-align: center;
    }
    .svg-canvas {
      width: 100%;
      height: auto;
      aspect-ratio: 4 / 3.2;
      display: block;
    }
    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 12px;
      width: 100%;
      max-width: 480px;
      margin-top: 14px;
    }
    .play-btn {
      background: #2563eb;
      color: #ffffff;
      border: none;
      border-radius: 6px;
      padding: 6px 14px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      display: flex;
      align-items: center;
      gap: 6px;
      user-select: none;
      transition: background 0.2s;
    }
    .play-btn:hover {
      background: #1d4ed8;
    }
    .slider-wrap {
      flex: 1;
      display: flex;
      align-items: center;
    }
    .slider {
      width: 100%;
      height: 6px;
      border-radius: 3px;
      background: #e2e8f0;
      outline: none;
      accent-color: #2563eb;
      cursor: pointer;
    }
    .badges {
      display: flex;
      flex-wrap: wrap;
      justify-content: center;
      gap: 8px;
      margin-top: 12px;
      width: 100%;
    }
    .badge {
      background: #f0fdf4;
      border: 1px solid #bbf7d0;
      color: #166534;
      font-size: 12px;
      font-weight: 600;
      padding: 4px 10px;
      border-radius: 9999px;
      display: flex;
      align-items: center;
      gap: 4px;
    }
    @media (max-width: 480px) {
      .diagram-grid {
        grid-template-columns: 1fr;
        gap: 8px;
      }
      .panel-title { font-size: 14px; }
      .panel-subtitle { font-size: 12px; }
      .svg-canvas { aspect-ratio: 16 / 9; }
    }
  </style>
</head>
<body>

  <div class="diagram-grid">
    
    <div class="panel">
      <div class="panel-title">Translation</div>
      <div class="panel-subtitle">Slide along vector</div>
      <svg class="svg-canvas" viewBox="0 0 160 120">
        <defs>
          <marker id="arrow" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
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          <marker id="arrow-gray" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="5" markerHeight="5" orient="auto-start-reverse">
            <path d="M 0 2 L 7 5 L 0 8 z" fill="#94a3b8"/>
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        </defs>

        
        <line id="t-traj1" x1="25" y1="95" x2="80" y2="60" stroke="#cbd5e1" stroke-dasharray="3,3" stroke-width="1.5" />
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        <text x="76" y="90" font-size="9" fill="#2563eb" font-weight="600">v⃗</text>
      </svg>
    </div>

    
    <div class="panel">
      <div class="panel-title">Rotation</div>
      <div class="panel-subtitle">90° turn around point</div>
      <svg class="svg-canvas" viewBox="0 0 160 120">
        
        <path d="M 45 42 A 48 48 0 0 1 115 50" fill="none" stroke="#94a3b8" stroke-dasharray="3,3" stroke-width="1.5" marker-end="url(#arrow-gray)" />

        
        <polygon points="45,80 45,40 75,80" fill="none" stroke="#93c5fd" stroke-width="1.5" stroke-dasharray="3,3" />

        
        <g id="rot-group">
          <polygon points="45,80 45,40 75,80" fill="rgba(37,99,235,0.22)" stroke="#2563eb" stroke-width="2" />
        </g>

        
        <circle cx="80" cy="80" r="3.5" fill="#1e2945" />
        <text x="80" y="96" font-size="9" fill="#64748b" font-weight="500" text-anchor="middle">Center</text>
      </svg>
    </div>

    
    <div class="panel">
      <div class="panel-title">Reflection</div>
      <div class="panel-subtitle">Flip across line</div>
      <svg class="svg-canvas" viewBox="0 0 160 120">
        
        <line x1="80" y1="12" x2="80" y2="108" stroke="#64748b" stroke-width="1.5" stroke-dasharray="4,3" />
        <text x="80" y="116" font-size="8" fill="#64748b" font-weight="500" text-anchor="middle">Line of reflection</text>

        
        <line x1="60" y1="90" x2="100" y2="90" stroke="#cbd5e1" stroke-dasharray="2,2" stroke-width="1" />
        <line x1="20" y1="90" x2="140" y2="90" stroke="#cbd5e1" stroke-dasharray="2,2" stroke-width="1" />
        <line x1="60" y1="40" x2="100" y2="40" stroke="#cbd5e1" stroke-dasharray="2,2" stroke-width="1" />

        
        <polygon points="60,90 20,90 60,40" fill="none" stroke="#93c5fd" stroke-width="1.5" stroke-dasharray="3,3" />

        
        <polygon id="refl-shape" points="60,90 20,90 60,40" fill="rgba(37,99,235,0.22)" stroke="#2563eb" stroke-width="2" />
      </svg>
    </div>
  </div>

  <div class="controls">
    <button id="playBtn" class="play-btn" aria-label="Play or Pause">
      <span id="playIcon">⏸</span>
      <span id="playLabel">Pause</span>
    </button>
    <div class="slider-wrap">
      <input type="range" id="scrubber" class="slider" min="0" max="1" step="0.005" value="0" aria-label="Animation progress">
    </div>
  </div>

  <div class="badges">
    <div class="badge"><span>✓</span> Side lengths preserved</div>
    <div class="badge"><span>✓</span> Angle measures preserved</div>
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</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Triangle Congruence: Rigid Transformations</title>
  <style>
    * {
      box-sizing: border-box;
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      padding: 0;
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      font-weight: 500;
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    .svg-container {
      width: 100%;
      max-width: 540px;
      display: flex;
      align-items: center;
      justify-content: center;
      margin: 4px 0 8px;
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    svg {
      width: 100%;
      height: auto;
      max-height: 240px;
      overflow: visible;
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    .controls {
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      gap: 8px;
      align-items: center;
      justify-content: center;
      flex-wrap: wrap;
    }
    .btn {
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      border: 1px solid #cbd5e1;
      color: #1e2945;
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      font-weight: 600;
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      min-width: 78px;
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      transform-origin: 0px 0px;
      transition: transform 0.85s cubic-bezier(0.4, 0, 0.2, 1);
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    #polyABC {
      transition: fill 0.45s ease, stroke 0.45s ease;
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    .label-abc {
      transition: opacity 0.3s ease;
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    .match-fade {
      transition: opacity 0.45s ease;
    }
    .glow-pulse {
      animation: pulseGlow 1.4s infinite alternate ease-in-out;
      transform-origin: center;
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    @keyframes pulseGlow {
      0% { transform: scale(0.85); opacity: 0.8; }
      100% { transform: scale(1.3); opacity: 0.25; }
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      .status-text { font-size: 12px; }
      .btn { padding: 5px 10px; font-size: 11.5px; }
      body { padding: 8px 10px 8px; }
    }
  </style>
</head>
<body>

  <div class="header-container">
    <div class="title">△ABC ≅ △DEF</div>
    <div class="status-text" id="stepDesc">1. Initial state: △ABC (blue) and △DEF (orange)</div>
  </div>

  <div class="svg-container">
    <svg viewBox="0 0 520 240" aria-label="Triangle Congruence Animation">
      <defs>
        
        <pattern id="grid" width="20" height="20" patternUnits="userSpaceOnUse">
          <path d="M 20 0 L 0 0 0 20" fill="none" stroke="#f1f5f9" stroke-width="1.5" />
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      </defs>

      
      <rect width="520" height="240" fill="url(#grid)" rx="8" />

      
      <path id="motionPath" d="M 100 70 Q 225 35 350 80" fill="none" stroke="#cbd5e1" stroke-width="1.75" stroke-dasharray="5 5" />
      <path d="M 342 75 L 350 80 L 344 87" fill="none" stroke="#94a3b8" stroke-width="1.75" stroke-linecap="round" stroke-linejoin="round" />

      
      <g id="triDEF" transform="translate(350, 80) rotate(52)">
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        <circle cx="35" cy="90" r="4.5" fill="#f97316" />
      </g>

      
      <text x="352" y="60" font-size="14" font-weight="700" fill="#ea580c" text-anchor="middle">D</text>
      <text x="444" y="190" font-size="14" font-weight="700" fill="#ea580c">E</text>
      <text x="310" y="174" font-size="14" font-weight="700" fill="#ea580c" text-anchor="end">F</text>

      
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          <circle cx="0" cy="0" r="4.5" fill="#10b981" />
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        <text class="label-abc" id="labelC" x="25" y="108" font-size="14" font-weight="700" fill="#2563eb" text-anchor="end">C</text>
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      <g id="matchBadges" class="match-fade" opacity="0">
        <text x="350" y="52" font-size="13" font-weight="800" fill="#059669" text-anchor="middle">A ≡ D</text>
        <text x="448" y="178" font-size="13" font-weight="800" fill="#059669">B ≡ E</text>
        <text x="280" y="168" font-size="13" font-weight="800" fill="#059669" text-anchor="end">C ≡ F</text>
      </g>
    </svg>
  </div>

  <div class="controls">
    <button class="btn active" id="btn0" onclick="goToStep(0)">1. Start</button>
    <button class="btn" id="btn1" onclick="goToStep(1)">2. Slide (Translate)</button>
    <button class="btn" id="btn2" onclick="goToStep(2)">3. Turn (Rotate)</button>
    <button class="btn btn-play" id="btnPlay" onclick="togglePlay()">⏸ Auto</button>
  </div>

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    const triABC = document.getElementById('triABC');
    const polyABC = document.getElementById('polyABC');
    const dotA = document.getElementById('dotA');
    const dotB = document.getElementById('dotB');
    const dotC = document.getElementById('dotC');
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      "3. Rotation (turn): rotate △ABC around A to perfectly superimpose on △DEF"
    ];

    let currentStep = 0;
    let isPlaying = true;
    let autoTimer = null;
    let badgeTimeout = null;

    function applyState(step) {
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      clearTimeout(badgeTimeout);

      buttons.forEach((b, i) => b.classList.toggle('active', i === step));
      stepDesc.textContent = descriptions[step];

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        triABC.style.transform = 'translate(100px, 70px) rotate(0deg)';
        polyABC.setAttribute('fill', 'rgba(37, 99, 235, 0.15)');
        polyABC.setAttribute('stroke', '#2563eb');
        dotA.setAttribute('fill', '#2563eb');
        dotB.setAttribute('fill', '#2563eb');
        dotC.setAttribute('fill', '#2563eb');
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        matchBadges.style.opacity = '0';
        labels.forEach(l => l.style.opacity = '1');
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        polyABC.setAttribute('stroke', '#2563eb');
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        dotB.setAttribute('fill', '#2563eb');
        dotC.setAttribute('fill', '#2563eb');
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        matchBadges.style.opacity = '0';
        labels.forEach(l => l.style.opacity = '1');
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          polyABC.setAttribute('stroke', '#10b981');
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          dotB.setAttribute('fill', '#10b981');
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</body>
</html>

全等图形与全等三角形：重合性与对应顶点

全等三角形的性质：对应边相等与对应角相等

全等判定基本事实一（SSS）：三边分别相等

SSS 的应用：作一个角等于已知角与网格作图

全等判定基本事实二（SAS）：两边及其夹角分别相等

易错辨析：为什么两边及其中一边的对角（SSA）不能判定全等

全等判定基本事实三（ASA）：两角及其夹边分别相等

全等判定定理（AAS）：两角及其中一组等角的对边相等

全等三角形的证明范式：利用全等证明线段与角相等

全等典型模型：平移型、轴对称型与对顶旋转型全等

综合拓展：双重全等证明与倍长中线辅助线构造

math

全等三角形的性质与判定（SSS、SAS、ASA、AAS）

Proving Triangles Congruent with SSS (Side-Side-Side)

Proving Triangles Congruent with SAS (Side-Angle-Side)

Proving Triangles Congruent with ASA (Angle-Side-Angle)

Proving Triangles Congruent with AAS (Angle-Angle-Side)

Triangle Congruence: HL Theorem for Right Triangles

Why SSA and AAA Fail as Congruence Criteria

Using Congruent Triangle Proofs in Problems

Equidistance from the Endpoints of a Segment to Points on Its Perpendicular Bisector

Triangle Congruence Criteria and Proofs

等腰三角形的性质（一）：等边对等角的几何证明

等腰三角形的性质（二）：顶角平分线、底边高与中线“三线合一”

等腰三角形的判定定理：等角对等边的证明与应用

等边三角形的性质：各边相等与三个内角都等于60°

等边三角形的判定定理：三角相等或含60°角的等腰三角形

分类讨论专题：等腰三角形中的顶角/底角与腰长/底边多解问题

模型拓展：等边三角形与60°旋转“手拉手”全等模型

等腰三角形与等边三角形的性质与判定

直角三角形的两锐角互余及其判定定理

直角三角形斜边上的中线定理：斜边中线等于斜边的一半

斜边中线定理的逆定理与线段倍分关系计算

含30°角的直角三角形性质：30°对边等于斜边一半

直角三角形全等判定定理（HL）：斜边、直角边分别相等

综合运用：HL 与 SSS、SAS、ASA、AAS 在几何证明中的选择策略

直角三角形的性质、判定与斜边中线

Geometric Dissection Proofs of the Pythagorean Theorem

Deriving the Pythagorean Theorem Using Similar Triangles

Proving and Applying the Converse of the Pythagorean Theorem

Classifying Acute, Right, and Obtuse Triangles Using Side Lengths

Solving Multi-Step 2D Problems with the Pythagorean Theorem

Applying the Pythagorean Theorem in 3D Space and Prisms

Deriving the Distance Formula from the Pythagorean Theorem

Finding Distance Between Two Points Using Pythagoras

Verifying Segment Congruence Using the Distance Formula

Pythagorean Theorem, 3D Applications, and Coordinate Distance

Understanding Congruence of Shapes

Conditions for Triangle Congruence (SSS, SAS, ASA, RHS)

Identifying Congruent Triangles

Understanding Similarity of Shapes

Conditions for Triangle Similarity

Identifying Similar Triangles

Congruence and Similarity of Triangles

Congruence and Similarity of Quadrilaterals

Properties of Quadrilaterals Using Congruent Triangles

Solving Problems with Quadrilateral Properties

Transformations and Congruence

Transformations and Similarity

Quadrilaterals and Geometric Transformations

Describing Position in Three Dimensions

Using 3D Coordinate Systems

Using Digital Tools to Solve Spatial Problems

Designing Algorithms to Test Congruency and Similarity

Spatial Reasoning and Computational Geometry

Conceptos de congruencia y figuras geométricas congruentes

Criterios de congruencia de triángulos: LAL, ALA, LLL y LLA

Demostraciones geométricas básicas con triángulos congruentes

Concepto de semejanza y razón de proporcionalidad

Criterios de semejanza de triángulos: AA, LLL y LAL

Teorema de Tales: segmentos proporcionales entre paralelas

Aplicaciones del teorema de Tales: medición indirecta de alturas

Congruencia y semejanza de triángulos con el teorema de Tales

Teorema de Pitágoras: demostración geométrica y algebraica

Cálculo de hipotenusa y catetos en triángulos rectángulos

Recíproco del teorema de Pitágoras y clasificación de triángulos

Resolución de problemas contextualizados con Pitágoras

Teoremas de las alturas y del cateto en el triángulo rectángulo

Razones trigonométricas en el triángulo rectángulo: seno, coseno y tangente

Cálculo de lados y ángulos usando trigonometría

Problemas de ángulos de elevación y de depresión

Geometría del triángulo rectángulo: Pitágoras, relaciones métricas y trigonometría

OGM.9.GEO.3

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