<!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: #ffffff;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 10px 12px;
      user-select: none;
    }

    .header-bar {
      display: flex;
      flex-wrap: wrap;
      align-items: center;
      justify-content: center;
      gap: 8px 16px;
      margin-bottom: 4px;
    }

    .formula-box {
      background: #f8fafc;
      border: 1.5px solid #e2e8f0;
      border-radius: 8px;
      padding: 6px 14px;
      font-size: 17px;
      font-weight: 700;
      display: flex;
      align-items: center;
      gap: 6px;
    }

    .pill {
      display: inline-flex;
      align-items: center;
      justify-content: center;
      padding: 2px 8px;
      border-radius: 6px;
      font-size: 15px;
      font-weight: 700;
    }
    .pill-d { background: #fef3c7; color: #b45309; border: 1px solid #fde68a; }
    .pill-ab { background: #dbeafe; color: #1d4ed8; border: 1px solid #bfdbfe; }

    .svg-container {
      width: 100%;
      max-width: 440px;
      flex: 1 1 auto;
      display: flex;
      align-items: center;
      justify-content: center;
    }

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

    .callout {
      font-size: 12px;
      font-weight: 600;
      fill: #475569;
    }
    .callout-title {
      font-size: 13px;
      font-weight: 700;
    }

    .interactive-bar {
      display: flex;
      gap: 8px;
      margin-top: 4px;
    }

    .toggle-btn {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      color: #334155;
      padding: 6px 14px;
      border-radius: 6px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      display: flex;
      align-items: center;
      gap: 6px;
      transition: background 0.2s ease, border-color 0.2s ease;
    }
    .toggle-btn:hover {
      background: #e2e8f0;
      border-color: #94a3b8;
    }
    .toggle-btn.active {
      background: #eff6ff;
      border-color: #3b82f6;
      color: #1d4ed8;
    }
  </style>
</head>
<body>

  
  <div class="header-bar">
    <div class="formula-box">
      <span class="pill pill-d">∠d</span>
      <span>=</span>
      <span class="pill pill-ab">∠a</span>
      <span>+</span>
      <span class="pill pill-ab">∠b</span>
    </div>
  </div>

  
  <div class="svg-container">
    <svg viewBox="0 0 440 240" aria-label="Exterior Angle Theorem Diagram">
      <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>
      </defs>

      
      <line x1="280" y1="180" x2="410" y2="180" stroke="#94a3b8" stroke-width="2.5" stroke-dasharray="5 4" marker-end="url(#arrow)" />

      
      <polygon points="140,45 60,180 280,180" fill="#f8fafc" stroke="#334155" stroke-width="2.5" stroke-linejoin="round" />

      
      <g transform="translate(15, 10)">
        <rect x="0" y="0" width="140" height="42" rx="6" fill="#eff6ff" stroke="#bfdbfe" stroke-width="1.2" />
        <text x="70" y="18" text-anchor="middle" class="callout-title" fill="#1d4ed8">Remote Interior</text>
        <text x="70" y="33" text-anchor="middle" class="callout" fill="#2563eb">Angles ∠a &amp; ∠b</text>
        
        <path d="M 120,42 Q 135,46 138,50" fill="none" stroke="#93c5fd" stroke-width="1.5" stroke-dasharray="3 3" />
        
        <path d="M 40,42 Q 40,110 58,165" fill="none" stroke="#93c5fd" stroke-width="1.5" stroke-dasharray="3 3" />
      </g>

      
      <g transform="translate(305, 75)">
        <rect x="0" y="0" width="125" height="42" rx="6" fill="#fef3c7" stroke="#fde68a" stroke-width="1.2" />
        <text x="62" y="18" text-anchor="middle" class="callout-title" fill="#b45309">Exterior Angle</text>
        <text x="62" y="33" text-anchor="middle" class="callout" fill="#d97706">Angle ∠d</text>
        
        <path d="M 40,42 Q 40,120 18,145" fill="none" stroke="#fcd34d" stroke-width="1.5" stroke-dasharray="3 3" />
      </g>

      
      <g id="proofLayer" opacity="0" style="transition: opacity 0.3s ease;">
        <line x1="280" y1="180" x2="350" y2="45" stroke="#3b82f6" stroke-width="2" stroke-dasharray="4 4" />
        <text x="355" y="55" font-size="11" font-weight="600" fill="#3b82f6">∥ side AB</text>
        
        <text x="306" y="125" font-size="13" font-weight="700" fill="#2563eb">a</text>
        
        <text x="330" y="168" font-size="13" font-weight="700" fill="#2563eb">b</text>
      </g>

      
      
      <path d="M 125,70 A 30 30 0 0 0 156,60" fill="none" stroke="#3b82f6" stroke-width="3" />
      <text x="140" y="85" text-anchor="middle" font-size="15" font-weight="700" fill="#2563eb">a</text>

      
      <path d="M 90,180 A 30 30 0 0 0 74,156" fill="none" stroke="#3b82f6" stroke-width="3" />
      <text x="88" y="168" font-size="15" font-weight="700" fill="#2563eb">b</text>

      
      <path d="M 252,180 A 28 28 0 0 1 262,162" fill="none" stroke="#64748b" stroke-width="2.5" />
      <text x="246" y="168" font-size="14" font-weight="700" fill="#64748b">c</text>

      
      <path d="M 262,162 A 34 34 0 0 1 314,180" fill="none" stroke="#f59e0b" stroke-width="3.5" />
      <text x="300" y="152" font-size="17" font-weight="800" fill="#d97706">d</text>

      
      <text x="140" y="32" text-anchor="middle" font-size="14" font-weight="700" fill="#1e2945">A</text>
      <text x="46" y="196" text-anchor="middle" font-size="14" font-weight="700" fill="#1e2945">B</text>
      <text x="274" y="200" text-anchor="middle" font-size="14" font-weight="700" fill="#1e2945">C</text>
      <text x="415" y="198" text-anchor="middle" font-size="14" font-weight="700" fill="#64748b">D</text>

      
      <path d="M 252,180 A 28 28 0 0 1 308,180" fill="none" stroke="#cbd5e1" stroke-width="1.5" stroke-dasharray="2 2" />
    </svg>
  </div>

  
  <div class="interactive-bar">
    <button id="proofBtn" class="toggle-btn">
      <span>✦</span>
      <span id="btnText">Show Why (d = a + b)</span>
    </button>
  </div>

  <script>
    const proofBtn = document.getElementById('proofBtn');
    const proofLayer = document.getElementById('proofLayer');
    const btnText = document.getElementById('btnText');
    let showingProof = false;

    proofBtn.addEventListener('click', () => {
      showingProof = !showingProof;
      if (showingProof) {
        proofLayer.setAttribute('opacity', '1');
        proofBtn.classList.add('active');
        btnText.textContent = 'Hide Parallel Line';
      } else {
        proofLayer.setAttribute('opacity', '0');
        proofBtn.classList.remove('active');
        btnText.textContent = 'Show Why (d = a + b)';
      }
    });
  </script>
</body>
</html>

Triangle Angle Sum and Exterior Angle Theorems

<!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, sans-serif;
      background: #f8fafc;
      color: #1e293b;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 12px 16px;
      user-select: none;
    }

    .header-badge {
      font-size: 15px;
      font-weight: 700;
      background: #ffffff;
      padding: 6px 14px;
      border-radius: 20px;
      border: 1px solid #e2e8f0;
      display: flex;
      align-items: center;
      gap: 8px;
      box-shadow: 0 1px 3px rgba(0,0,0,0.05);
    }

    .c-blue { color: #3b82f6; font-weight: 800; }
    .c-green { color: #10b981; font-weight: 800; }

    .svg-container {
      width: 100%;
      max-width: 440px;
      flex: 1;
      display: flex;
      align-items: center;
      justify-content: center;
    }

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

    .line-parallel {
      stroke: #475569;
      stroke-width: 2.5;
      stroke-linecap: round;
    }

    .line-transversal {
      stroke: #64748b;
      stroke-width: 2.5;
      stroke-linecap: round;
    }

    .arrow-marker {
      fill: none;
      stroke: #94a3b8;
      stroke-width: 2;
      stroke-linecap: round;
      stroke-linejoin: round;
    }

    .angle-label {
      font-size: 14px;
      font-weight: 700;
      dominant-baseline: central;
      text-anchor: middle;
    }

    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 12px;
      width: 100%;
      max-width: 380px;
      background: #ffffff;
      padding: 8px 16px;
      border-radius: 12px;
      border: 1px solid #e2e8f0;
      box-shadow: 0 1px 3px rgba(0,0,0,0.05);
    }

    .control-label {
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
    }

    input[type="range"] {
      flex: 1;
      accent-color: #3b82f6;
      cursor: pointer;
      height: 6px;
    }

    .btn-match {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      color: #334155;
      padding: 4px 10px;
      border-radius: 6px;
      font-size: 12px;
      font-weight: 600;
      cursor: pointer;
      display: flex;
      align-items: center;
      gap: 4px;
    }

    .btn-match:active {
      background: #e2e8f0;
    }
  </style>
</head>
<body>

  <div class="header-badge">
    <span>Alternate Interior:</span>
    <span><span class="c-blue">∠1</span> = <span class="c-green">∠2</span> = <span id="angleValue">56°</span></span>
  </div>

  <div class="svg-container">
    <svg viewBox="0 0 400 210">
      
      <line x1="25" y1="55" x2="375" y2="55" class="line-parallel" />
      <line x1="25" y1="155" x2="375" y2="155" class="line-parallel" />

      
      <path d="M 195 50 L 205 55 L 195 60" class="arrow-marker" />
      <path d="M 195 150 L 205 155 L 195 160" class="arrow-marker" />

      
      <text x="382" y="58" font-size="12" fill="#94a3b8" font-style="italic" font-weight="600">L₁</text>
      <text x="382" y="158" font-size="12" fill="#94a3b8" font-style="italic" font-weight="600">L₂</text>

      
      <line id="transversalLine" class="line-transversal" />

      
      <path id="angle1Arc" fill="#3b82f6" fill-opacity="0.22" stroke="#3b82f6" stroke-width="2.5" />
      
      <path id="angle2Arc" fill="#10b981" fill-opacity="0.22" stroke="#10b981" stroke-width="2.5" />

      
      <path id="overlayArc" fill="#3b82f6" fill-opacity="0.5" stroke="#2563eb" stroke-width="2.5" style="display: none;" />

      
      <text id="label1" class="angle-label" fill="#2563eb">∠1</text>
      <text id="label2" class="angle-label" fill="#059669">∠2</text>
    </svg>
  </div>

  <div class="controls">
    <span class="control-label">Transversal</span>
    <input type="range" id="angleSlider" min="35" max="75" value="56">
    <button class="btn-match" id="matchBtn">↺ Match</button>
  </div>

  <script>
    const y1 = 55;
    const y2 = 155;
    const cy = 105;
    const cx = 200;
    const r = 36;

    const slider = document.getElementById('angleSlider');
    const angleValue = document.getElementById('angleValue');
    const transversalLine = document.getElementById('transversalLine');
    const angle1Arc = document.getElementById('angle1Arc');
    const angle2Arc = document.getElementById('angle2Arc');
    const overlayArc = document.getElementById('overlayArc');
    const label1 = document.getElementById('label1');
    const label2 = document.getElementById('label2');
    const matchBtn = document.getElementById('matchBtn');

    let currentAngle = 56;
    let animProgress = 0;
    let isAnimating = false;

    function polarToCartesian(x, y, radius, angleInDegrees) {
      const rad = (angleInDegrees * Math.PI) / 180.0;
      return {
        x: x + radius * Math.cos(rad),
        y: y + radius * Math.sin(rad)
      };
    }

    function describeArc(x, y, radius, startAngle, endAngle) {
      const start = polarToCartesian(x, y, radius, startAngle);
      const end = polarToCartesian(x, y, radius, endAngle);
      return [
        "M", x, y,
        "L", start.x, start.y,
        "A", radius, radius, 0, 0, 1, end.x, end.y,
        "Z"
      ].join(" ");
    }

    function update() {
      const deg = parseFloat(slider.value);
      currentAngle = deg;
      angleValue.textContent = deg + "°";

      const rad = (deg * Math.PI) / 180;
      const dx = (cy - y1) / Math.tan(rad);

      const p1x = cx - dx;
      const p1y = y1;

      const p2x = cx + dx;
      const p2y = y2;

      // Extend transversal endpoints
      const extend = 32;
      const tx1 = p1x - extend * Math.cos(rad);
      const ty1 = p1y - extend * Math.sin(rad);
      const tx2 = p2x + extend * Math.cos(rad);
      const ty2 = p2y + extend * Math.sin(rad);

      transversalLine.setAttribute('x1', tx1);
      transversalLine.setAttribute('y1', ty1);
      transversalLine.setAttribute('x2', tx2);
      transversalLine.setAttribute('y2', ty2);

      // Angle 1: below L1, right of transversal (0° to deg)
      angle1Arc.setAttribute('d', describeArc(p1x, p1y, r, 0, deg));
      const mid1 = polarToCartesian(p1x, p1y, r + 16, deg / 2);
      label1.setAttribute('x', mid1.x);
      label1.setAttribute('y', mid1.y);

      // Angle 2: above L2, left of transversal (180° to 180° + deg)
      angle2Arc.setAttribute('d', describeArc(p2x, p2y, r, 180, 180 + deg));
      const mid2 = polarToCartesian(p2x, p2y, r + 16, 180 + deg / 2);
      label2.setAttribute('x', mid2.x);
      label2.setAttribute('y', mid2.y);
    }

    function animateMatch() {
      if (isAnimating) return;
      isAnimating = true;
      overlayArc.style.display = 'block';
      
      const startTime = performance.now();
      const duration = 1200;

      function step(now) {
        const elapsed = now - startTime;
        let t = Math.min(elapsed / duration, 1);
        // Smooth easeInOut
        t = t < 0.5 ? 2 * t * t : -1 + (4 - 2 * t) * t;

        const deg = currentAngle;
        const rad = (deg * Math.PI) / 180;
        const dx = (cy - y1) / Math.tan(rad);
        
        const p1x = cx - dx;
        const p2x = cx + dx;

        // Rotate 180 deg around center (cx, cy)
        const curAngleRot = t * 180;
        const originX = p1x + (p2x - p1x) * t;
        const originY = y1 + (y2 - y1) * t;

        overlayArc.setAttribute('d', describeArc(originX, originY, r, curAngleRot, curAngleRot + deg));

        if (t < 1) {
          requestAnimationFrame(step);
        } else {
          setTimeout(() => {
            overlayArc.style.display = 'none';
            isAnimating = false;
          }, 400);
        }
      }

      requestAnimationFrame(step);
    }

    slider.addEventListener('input', update);
    matchBtn.addEventListener('click', animateMatch);

    update();
  </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">
  <title>Triangle Angle Sum Proof</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }
    body {
      width: 100%;
      background: #ffffff;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e293b;
      display: flex;
      flex-direction: column;
      align-items: center;
      padding: 12px;
    }
    .diagram-wrap {
      width: 100%;
      max-width: 520px;
      display: flex;
      flex-direction: column;
      align-items: center;
    }
    svg {
      width: 100%;
      height: auto;
      display: block;
      overflow: visible;
    }
    .step-nav {
      display: flex;
      gap: 6px;
      margin-top: 10px;
      width: 100%;
      justify-content: center;
    }
    .step-btn {
      flex: 1;
      max-width: 130px;
      padding: 6px 8px;
      font-size: 13px;
      font-weight: 600;
      border: 1px solid #cbd5e1;
      border-radius: 6px;
      background: #f8fafc;
      color: #475569;
      cursor: pointer;
      text-align: center;
      transition: background 0.2s, color 0.2s, border-color 0.2s;
    }
    .step-btn.active {
      background: #2563eb;
      color: #ffffff;
      border-color: #2563eb;
    }
    .proof-display {
      margin-top: 10px;
      width: 100%;
      min-height: 48px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      display: flex;
      align-items: center;
      justify-content: center;
      padding: 8px 12px;
      text-align: center;
      font-size: 15px;
      font-weight: 600;
    }
    .angle-tag {
      display: inline-block;
      padding: 2px 6px;
      border-radius: 4px;
      margin: 0 2px;
      font-weight: 700;
    }
    .tag-blue { background: #dbeafe; color: #1d4ed8; }
    .tag-purple { background: #f3e8ff; color: #7e22ce; }
    .tag-emerald { background: #d1fae5; color: #047857; }

    /* SVG Transitions */
    .highlight-group {
      transition: opacity 0.3s ease;
    }
    .faded {
      opacity: 0.25;
    }
  </style>
</head>
<body>

<div class="diagram-wrap">
  <svg viewBox="0 0 500 240" aria-label="Proof of Triangle Angle Sum Theorem">
    <defs>
      
      <marker id="arrow-blue" markerWidth="6" markerHeight="6" refX="5" refY="3" orient="auto">
        <path d="M0,0 L6,3 L0,6 Z" fill="#2563eb" />
      </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="#059669" />
      </marker>
    </defs>

    
    <line x1="40" y1="60" x2="460" y2="60" stroke="#64748b" stroke-width="2" stroke-dasharray="6,4" />
    
    
    <polygon points="250,60 100,200 400,200" fill="#f8fafc" stroke="#1e293b" stroke-width="2.5" />

    
    
    <path id="wedge4" d="M 250,60 L 205,60 A 45 45 0 0 1 219.2 92.8 Z" fill="#3b82f6" fill-opacity="0.25" stroke="#2563eb" stroke-width="1.5" />
    
    <path id="wedge1" d="M 250,60 L 219.2 92.8 A 45 45 0 0 1 280.8 92.8 Z" fill="#a855f7" fill-opacity="0.25" stroke="#7c3aed" stroke-width="1.5" />
    
    <path id="wedge5" d="M 250,60 L 280.8 92.8 A 45 45 0 0 1 295,60 Z" fill="#10b981" fill-opacity="0.25" stroke="#059669" stroke-width="1.5" />

    
    <path id="wedge2" d="M 100,200 L 145,200 A 45 45 0 0 0 130.8 167.2 Z" fill="#3b82f6" fill-opacity="0.25" stroke="#2563eb" stroke-width="1.5" />
    
    <path id="wedge3" d="M 400,200 L 369.2 167.2 A 45 45 0 0 0 355,200 Z" fill="#10b981" fill-opacity="0.25" stroke="#059669" stroke-width="1.5" />

    
    <g id="relation-arrows" class="highlight-group">
      <path d="M 195,78 Q 140,110 132,160" fill="none" stroke="#2563eb" stroke-width="2" stroke-dasharray="4,4" marker-end="url(#arrow-blue)" />
      <path d="M 305,78 Q 360,110 368,160" fill="none" stroke="#059669" stroke-width="2" stroke-dasharray="4,4" marker-end="url(#arrow-green)" />
    </g>

    
    <text id="lbl4" x="210" y="52" fill="#1d4ed8" font-size="14" font-weight="700" text-anchor="middle">∠4</text>
    <text id="lbl1" x="250" y="105" fill="#7e22ce" font-size="14" font-weight="700" text-anchor="middle">∠1</text>
    <text id="lbl5" x="290" y="52" fill="#047857" font-size="14" font-weight="700" text-anchor="middle">∠5</text>
    <text id="lbl2" x="140" y="190" fill="#1d4ed8" font-size="14" font-weight="700">∠2</text>
    <text id="lbl3" x="342" y="190" fill="#047857" font-size="14" font-weight="700">∠3</text>

    
    <text x="250" y="42" fill="#1e293b" font-size="14" font-weight="700" text-anchor="middle">A</text>
    <text x="85" y="215" fill="#1e293b" font-size="14" font-weight="700">B</text>
    <text x="408" y="215" fill="#1e293b" font-size="14" font-weight="700">C</text>

    
    <path d="M 70,56 L 76,60 L 70,64 M 76,56 L 82,60 L 76,64" fill="none" stroke="#64748b" stroke-width="1.5" />
    <path d="M 235,196 L 241,200 L 235,204 M 241,196 L 247,200 L 241,204" fill="none" stroke="#64748b" stroke-width="1.5" />
  </svg>

  
  <div class="step-nav">
    <button class="step-btn active" onclick="setStep(0)">1. Straight Line</button>
    <button class="step-btn" onclick="setStep(1)">2. Alternate ∠s</button>
    <button class="step-btn" onclick="setStep(2)">3. Triangle Sum</button>
  </div>

  
  <div class="proof-display" id="proofText">
    <span><span class="angle-tag tag-blue">∠4</span> + <span class="angle-tag tag-purple">∠1</span> + <span class="angle-tag tag-emerald">∠5</span> = 180°</span>
  </div>
</div>

<script>
  const steps = [
    {
      text: '<span><span class="angle-tag tag-blue">∠4</span> + <span class="angle-tag tag-purple">∠1</span> + <span class="angle-tag tag-emerald">∠5</span> = 180° (straight line at A)</span>',
      fade: ['wedge2', 'wedge3', 'lbl2', 'lbl3', 'relation-arrows']
    },
    {
      text: '<span><span class="angle-tag tag-blue">∠4 = ∠2</span> and <span class="angle-tag tag-emerald">∠5 = ∠3</span> (alternate interior angles)</span>',
      fade: ['wedge1', 'lbl1']
    },
    {
      text: '<span><span class="angle-tag tag-blue">∠2</span> + <span class="angle-tag tag-purple">∠1</span> + <span class="angle-tag tag-emerald">∠3</span> = 180° (by substitution)</span>',
      fade: ['wedge4', 'wedge5', 'lbl4', 'lbl5', 'relation-arrows']
    }
  ];

  const allElements = ['wedge1', 'wedge2', 'wedge3', 'wedge4', 'wedge5', 'lbl1', 'lbl2', 'lbl3', 'lbl4', 'lbl5', 'relation-arrows'];
  let currentStep = 0;
  let timer = null;

  function setStep(index) {
    currentStep = index;
    const btns = document.querySelectorAll('.step-btn');
    btns.forEach((btn, i) => btn.classList.toggle('active', i === index));

    const cfg = steps[index];
    document.getElementById('proofText').innerHTML = cfg.text;

    allElements.forEach(id => {
      const el = document.getElementById(id);
      if (el) {
        el.classList.toggle('faded', cfg.fade.includes(id));
      }
    });
  }

  function autoPlay() {
    timer = setInterval(() => {
      setStep((currentStep + 1) % steps.length);
    }, 4000);
  }

  // Initial state
  setStep(0);
  autoPlay();

  // Pause auto-play on manual interaction
  document.querySelectorAll('.step-btn').forEach(btn => {
    btn.addEventListener('click', () => {
      clearInterval(timer);
    });
  });
</script>

</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Congruent Angles - Rigid Motion</title>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      width: 100%;
      min-height: 100%;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #ffffff;
      color: #1e293b;
      display: flex;
      flex-direction: column;
      align-items: center;
      padding: 12px 10px;
      user-select: none;
      -webkit-user-select: none;
    }

    .header-bar {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 10px;
      flex-wrap: wrap;
      margin-bottom: 6px;
      width: 100%;
      max-width: 520px;
    }

    .stat-chip {
      background: #f8fafc;
      border: 1.5px solid #94a3b8;
      padding: 5px 12px;
      border-radius: 6px;
      font-size: 13px;
      font-weight: 700;
      color: #0369a1;
      letter-spacing: 0.2px;
    }

    .congruence-chip {
      background: #e0f2fe;
      border: 1.5px solid #0284c7;
      padding: 5px 14px;
      border-radius: 6px;
      font-size: 14px;
      font-weight: 800;
      color: #0369a1;
      transition: background-color 0.3s ease, border-color 0.3s ease, color 0.3s ease, box-shadow 0.3s ease;
    }

    .congruence-chip.highlight {
      background: #dcfce7;
      border-color: #16a34a;
      color: #15803d;
      box-shadow: 0 0 10px rgba(22, 163, 74, 0.3);
    }

    .svg-container {
      width: 100%;
      max-width: 520px;
      position: relative;
    }

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

    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      margin-top: 10px;
      width: 100%;
      max-width: 520px;
      flex-wrap: wrap;
    }

    .btn {
      appearance: none;
      border: 1.5px solid #94a3b8;
      background: #f8fafc;
      color: #1e293b;
      font-size: 13px;
      font-weight: 600;
      padding: 6px 14px;
      border-radius: 6px;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      gap: 5px;
      transition: background-color 0.15s, border-color 0.15s, color 0.15s;
    }

    .btn:hover {
      background: #e2e8f0;
      border-color: #64748b;
    }

    .btn.active {
      background: #0284c7;
      border-color: #0284c7;
      color: #ffffff;
    }

    .btn.active:hover {
      background: #0369a1;
      border-color: #0369a1;
    }

    .btn-play {
      background: #0284c7;
      border-color: #0284c7;
      color: #ffffff;
      padding: 6px 16px;
    }

    .btn-play:hover {
      background: #0369a1;
      border-color: #0369a1;
    }

    .status-text {
      font-size: 13px;
      font-weight: 600;
      color: #475569;
      margin-top: 6px;
      text-align: center;
      min-height: 20px;
    }
  </style>
</head>
<body>

  <div class="header-bar">
    <div class="stat-chip">m∠ABC = 50°</div>
    <div class="stat-chip">m∠DEF = 50°</div>
    <div class="congruence-chip" id="resultChip">∠ABC ≅ ∠DEF</div>
  </div>

  <div class="svg-container">
    <svg viewBox="0 0 520 280" xmlns="http://www.w3.org/2000/svg">
      <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="#1e293b" />
        </marker>
        <marker id="arrow-blue" 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="#0284c7" />
        </marker>

        
        <filter id="paper-shadow" x="-20%" y="-20%" width="140%" height="140%">
          <feDropShadow dx="0" dy="2" stdDeviation="3" flood-color="#0284c7" flood-opacity="0.25" />
        </filter>
      </defs>

      
      <path id="motionPath" d="M 120 215 C 200 130, 270 140, 370 175" fill="none" stroke="#64748b" stroke-width="1.5" stroke-dasharray="4 4" opacity="0.75" />

      
      <g id="angleDEF">
        
        <g id="protDEF">
          
          <g transform="translate(370, 175) rotate(-35)">
            
            <path d="M -70 0 A 70 70 0 0 1 70 0 Z" fill="#f1f5f9" stroke="#64748b" stroke-width="1.5" />
            <path d="M -50 0 A 50 50 0 0 1 50 0 Z" fill="#ffffff" stroke="#94a3b8" stroke-width="1.2" />
            
            <line x1="0" y1="0" x2="68" y2="0" stroke="#334155" stroke-width="1.5" />
            <line x1="0" y1="0" x2="43.7" y2="-52.1" stroke="#0284c7" stroke-width="2" />
            
            <path d="M 0 0 L 48 0 A 48 48 0 0 0 30.85 -36.77 Z" fill="rgba(2, 132, 199, 0.18)" />
            
            <text x="56" y="11" font-size="10" fill="#1e293b" font-weight="700" text-anchor="middle">0°</text>
            <text x="36" y="-42" font-size="10" fill="#0369a1" font-weight="800" text-anchor="middle">50°</text>
            <text x="0" y="-55" font-size="10" fill="#1e293b" font-weight="700" text-anchor="middle">90°</text>
            <circle cx="0" cy="0" r="2.5" fill="#334155" />
          </g>
        </g>

        
        
        <line x1="370" y1="175" x2="464.2" y2="109" stroke="#1e293b" stroke-width="2.5" stroke-linecap="round" marker-end="url(#arrow)" />
        
        <line x1="370" y1="175" x2="380" y2="60.4" stroke="#1e293b" stroke-width="2.5" stroke-linecap="round" marker-end="url(#arrow)" />

        
        <path d="M 396.2 156.6 A 32 32 0 0 0 372.8 143.1" fill="none" stroke="#0284c7" stroke-width="2.5" stroke-linecap="round" />
        
        
        <circle cx="370" cy="175" r="3.5" fill="#1e293b" />

        
        <circle cx="442" cy="124.6" r="2.5" fill="#1e293b" />
        <text x="454" y="132" font-size="13" font-weight="700" fill="#1e293b">F</text>

        <circle cx="377.8" cy="85" r="2.5" fill="#1e293b" />
        <text x="365" y="80" font-size="13" font-weight="700" fill="#1e293b">D</text>

        <text x="352" y="195" font-size="14" font-weight="700" fill="#1e293b">E</text>
        <text x="404" y="138" font-size="12" font-weight="800" fill="#0369a1">50°</text>
      </g>

      
      <g id="angleABC">
        
        <g id="protABC">
          <g transform="translate(120, 215)">
            <path d="M -70 0 A 70 70 0 0 1 70 0 Z" fill="#f1f5f9" stroke="#64748b" stroke-width="1.5" />
            <path d="M -50 0 A 50 50 0 0 1 50 0 Z" fill="#ffffff" stroke="#94a3b8" stroke-width="1.2" />
            <line x1="0" y1="0" x2="68" y2="0" stroke="#334155" stroke-width="1.5" />
            <line x1="0" y1="0" x2="43.7" y2="-52.1" stroke="#0284c7" stroke-width="2" />
            <path d="M 0 0 L 48 0 A 48 48 0 0 0 30.85 -36.77 Z" fill="rgba(2, 132, 199, 0.18)" />
            <text x="56" y="11" font-size="10" fill="#1e293b" font-weight="700" text-anchor="middle">0°</text>
            <text x="36" y="-42" font-size="10" fill="#0369a1" font-weight="800" text-anchor="middle">50°</text>
            <text x="0" y="-55" font-size="10" fill="#1e293b" font-weight="700" text-anchor="middle">90°</text>
            <circle cx="0" cy="0" r="2.5" fill="#334155" />
          </g>
        </g>

        
        <line x1="120" y1="215" x2="235" y2="215" stroke="#1e293b" stroke-width="2.5" stroke-linecap="round" marker-end="url(#arrow)" />
        <line x1="120" y1="215" x2="193.9" y2="126.9" stroke="#1e293b" stroke-width="2.5" stroke-linecap="round" marker-end="url(#arrow)" />

        
        <path d="M 152 215 A 32 32 0 0 0 140.6 190.5" fill="none" stroke="#0284c7" stroke-width="2.5" stroke-linecap="round" />

        
        <circle cx="120" cy="215" r="3.5" fill="#1e293b" />

        
        <circle cx="205" cy="215" r="2.5" fill="#1e293b" />
        <text x="205" y="233" font-size="13" font-weight="700" fill="#1e293b">C</text>

        <circle cx="173" cy="152" r="2.5" fill="#1e293b" />
        <text x="160" y="142" font-size="13" font-weight="700" fill="#1e293b">A</text>

        <text x="102" y="228" font-size="14" font-weight="700" fill="#1e293b">B</text>
        <text x="156" y="196" font-size="12" font-weight="800" fill="#0369a1">50°</text>
      </g>

      
      <g id="ghostContainer">
        <g id="ghostLayer" opacity="0" pointer-events="none">
          
          <polygon points="90,240 245,240 215,95 75,150" fill="rgba(224, 242, 254, 0.75)" stroke="#0284c7" stroke-width="1.5" stroke-dasharray="3 3" filter="url(#paper-shadow)" />

          
          <line x1="120" y1="215" x2="235" y2="215" stroke="#0284c7" stroke-width="3" stroke-linecap="round" marker-end="url(#arrow-blue)" />
          
          <line x1="120" y1="215" x2="193.9" y2="126.9" stroke="#0284c7" stroke-width="3" stroke-linecap="round" marker-end="url(#arrow-blue)" />
          
          <path d="M 152 215 A 32 32 0 0 0 140.6 190.5" fill="none" stroke="#0284c7" stroke-width="3" />

          
          <circle cx="120" cy="215" r="4" fill="#0284c7" />
          <text x="96" y="210" font-size="12" font-weight="800" fill="#0369a1">ABC</text>
        </g>
      </g>

      
      <g id="matchGlow" opacity="0" transform="translate(370, 175) rotate(-35)">
        <path d="M 0 0 L 115 0" stroke="#16a34a" stroke-width="4" stroke-linecap="round" opacity="0.9" />
        <path d="M 0 0 L 73.9 -88.1" stroke="#16a34a" stroke-width="4" stroke-linecap="round" opacity="0.9" />
        <circle cx="0" cy="0" r="5" fill="#16a34a" />
      </g>
    </svg>
  </div>

  <div class="status-text" id="statusText">Both angles measure exactly 50°</div>

  <div class="controls">
    <button class="btn active" id="btnStep1" onclick="setStep(1)">1. Separate</button>
    <button class="btn" id="btnStep2" onclick="setStep(2)">2. Superimpose</button>
    <button class="btn btn-play" id="btnPlay" onclick="togglePlay()">▶ Play</button>
  </div>

  <script>
    const ghostContainer = document.getElementById('ghostContainer');
    const ghostLayer = document.getElementById('ghostLayer');
    const matchGlow = document.getElementById('matchGlow');
    const resultChip = document.getElementById('resultChip');
    const statusText = document.getElementById('statusText');
    const btnStep1 = document.getElementById('btnStep1');
    const btnStep2 = document.getElementById('btnStep2');
    const btnPlay = document.getElementById('btnPlay');

    let isPlaying = false;
    let animProgress = 0; // 0 to 1
    let animStartTime = null;
    let animReqId = null;
    const TOTAL_DURATION = 2200; // ms

    // Easing helper
    function easeInOutQuad(t) {
      return t < 0.5 ? 2 * t * t : -1 + (4 - 2 * t) * t;
    }

    function renderState(p) {
      animProgress = Math.max(0, Math.min(1, p));

      // Ghost opacity: fade in between 0.0 and 0.2
      let opacity = 0;
      if (animProgress > 0) {
        opacity = Math.min(1, animProgress / 0.15);
      }
      ghostLayer.setAttribute('opacity', opacity);

      // Translation and rotation:
      // dx from 0 to 250, dy from 0 to -40, rotate from 0 to -35 deg around (120, 215)
      const moveProgress = easeInOutQuad(Math.max(0, Math.min(1, animProgress)));
      const dx = 250 * moveProgress;
      const dy = -40 * moveProgress;
      const rot = -35 * moveProgress;

      ghostContainer.setAttribute(
        'transform',
        `translate(${dx}, ${dy}) rotate(${rot}, 120, 215)`
      );

      // Match glow and highlight near completion
      if (animProgress >= 0.95) {
        const glowProg = (animProgress - 0.95) / 0.05;
        matchGlow.setAttribute('opacity', glowProg);
        resultChip.className = 'congruence-chip highlight';
      } else {
        matchGlow.setAttribute('opacity', 0);
        resultChip.className = 'congruence-chip';
      }
    }

    function animLoop(timestamp) {
      if (!animStartTime) animStartTime = timestamp - (animProgress * TOTAL_DURATION);
      const elapsed = timestamp - animStartTime;
      const p = Math.min(1, elapsed / TOTAL_DURATION);

      renderState(p);

      if (p < 1) {
        animReqId = requestAnimationFrame(animLoop);
      } else {
        isPlaying = false;
        btnPlay.innerHTML = '▶ Replay';
        btnStep1.classList.remove('active');
        btnStep2.classList.add('active');
        statusText.textContent = 'Perfect match! ∠ABC ≅ ∠DEF (Rigid motion)';
      }
    }

    function setStep(step) {
      if (isPlaying) {
        cancelAnimationFrame(animReqId);
        isPlaying = false;
        btnPlay.innerHTML = '▶ Play';
      }

      if (step === 1) {
        btnStep1.classList.add('active');
        btnStep2.classList.remove('active');
        statusText.textContent = 'Both angles measure exactly 50°';
        renderState(0);
      } else {
        btnStep2.classList.add('active');
        btnStep1.classList.remove('active');
        statusText.textContent = 'Tracing paper overlay fits with zero overhang!';
        renderState(1);
      }
    }

    function togglePlay() {
      if (isPlaying) {
        cancelAnimationFrame(animReqId);
        isPlaying = false;
        btnPlay.innerHTML = '▶ Play';
      } else {
        if (animProgress >= 1) {
          animProgress = 0;
          renderState(0);
        }
        isPlaying = true;
        btnPlay.innerHTML = '⏸ Pause';
        btnStep1.classList.remove('active');
        btnStep2.classList.add('active');
        statusText.textContent = 'Translating and rotating ∠ABC onto ∠DEF...';
        animStartTime = null;
        animReqId = requestAnimationFrame(animLoop);
      }
    }

    // Initialize state
    renderState(0);
  </script>
</body>
</html>

Congruence of Line Segments and Angles

<!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: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
      color: #1e2945;
      background: #ffffff;
      padding: 12px;
      display: flex;
      flex-direction: column;
      gap: 12px;
    }

    /* Concept Rule Banner */
    .rule-bar {
      display: flex;
      justify-content: center;
      gap: 8px;
      flex-wrap: wrap;
    }

    .rule-chip {
      display: inline-flex;
      align-items: center;
      gap: 6px;
      font-size: 13px;
      font-weight: 600;
      padding: 5px 12px;
      border-radius: 20px;
      background: #f1f5f9;
      color: #475569;
      border: 1px solid #e2e8f0;
    }

    .rule-chip strong {
      color: #0f172a;
    }

    .chip-eq {
      border-color: #cbd5e1;
      background: #f8fafc;
    }

    .chip-cong {
      border-color: #cbd5e1;
      background: #f8fafc;
    }

    /* Comparison Grid */
    .comparison-grid {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 12px;
      align-items: start;
    }

    @media (max-width: 380px) {
      .comparison-grid {
        grid-template-columns: 1fr;
      }
    }

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

    .col-header {
      display: flex;
      align-items: center;
      gap: 6px;
      font-size: 14px;
      font-weight: 700;
      padding: 8px 12px;
      border-radius: 8px;
    }

    .col-header.correct {
      background: #ecfdf5;
      color: #065f46;
      border: 1px solid #a7f3d0;
    }

    .col-header.incorrect {
      background: #fef2f2;
      color: #991b1b;
      border: 1px solid #fecaca;
    }

    .card-item {
      background: #ffffff;
      border-radius: 8px;
      padding: 10px 12px;
      display: flex;
      flex-direction: column;
      gap: 4px;
      transition: background-color 0.2s ease, border-color 0.2s ease;
      cursor: pointer;
    }

    .card-item.correct-card {
      border: 1px solid #bbf7d0;
      background: #f0fdf4;
    }

    .card-item.correct-card:hover {
      background: #dcfce7;
      border-color: #86efac;
    }

    .card-item.incorrect-card {
      border: 1px solid #fecaca;
      background: #fff5f5;
    }

    .card-item.incorrect-card:hover {
      background: #fee2e2;
      border-color: #fca5a5;
    }

    .card-header-row {
      display: flex;
      align-items: center;
      justify-content: space-between;
    }

    .math-expr {
      font-size: 16px;
      font-weight: 700;
      font-family: "Cambria Math", "KaTeX_Main", "Times New Roman", serif;
      letter-spacing: 0.5px;
    }

    .overbar {
      text-decoration: overline;
      display: inline-block;
    }

    .icon-badge {
      font-size: 14px;
      font-weight: 800;
      line-height: 1;
    }

    .icon-badge.check {
      color: #16a34a;
    }

    .icon-badge.cross {
      color: #dc2626;
    }

    .desc-tag {
      font-size: 11.5px;
      font-weight: 500;
      line-height: 1.3;
    }

    .correct-card .desc-tag {
      color: #15803d;
    }

    .incorrect-card .desc-tag {
      color: #b91c1c;
    }

    /* Filter Controls */
    .filter-bar {
      display: flex;
      justify-content: center;
      gap: 6px;
    }

    .filter-btn {
      background: #f1f5f9;
      border: 1px solid #e2e8f0;
      color: #475569;
      font-size: 12px;
      font-weight: 600;
      padding: 4px 12px;
      border-radius: 6px;
      cursor: pointer;
      transition: all 0.2s ease;
    }

    .filter-btn.active {
      background: #2563eb;
      color: #ffffff;
      border-color: #2563eb;
    }
  </style>
</head>
<body>

  
  <div class="rule-bar">
    <div class="rule-chip chip-eq">
      <span>Numbers & Measures:</span>
      <strong>=</strong>
    </div>
    <div class="rule-chip chip-cong">
      <span>Geometric Shapes:</span>
      <strong>≅</strong>
    </div>
  </div>

  
  <div class="filter-bar">
    <button class="filter-btn active" onclick="filterCategory('all', this)">All</button>
    <button class="filter-btn" onclick="filterCategory('segment', this)">Segments</button>
    <button class="filter-btn" onclick="filterCategory('angle', this)">Angles</button>
  </div>

  
  <div class="comparison-grid">
    
    
    <div class="column">
      <div class="col-header correct">
        <span>✓</span>
        <span>Correct Notation</span>
      </div>

      
      <div class="card-item correct-card" data-cat="segment">
        <div class="card-header-row">
          <span class="math-expr">AB = CD</span>
          <span class="icon-badge check">✓</span>
        </div>
        <span class="desc-tag">Lengths are equal (numbers)</span>
      </div>

      
      <div class="card-item correct-card" data-cat="segment">
        <div class="card-header-row">
          <span class="math-expr"><span class="overbar">AB</span> ≅ <span class="overbar">CD</span></span>
          <span class="icon-badge check">✓</span>
        </div>
        <span class="desc-tag">Segments are congruent (shapes)</span>
      </div>

      
      <div class="card-item correct-card" data-cat="angle">
        <div class="card-header-row">
          <span class="math-expr">m∠A = m∠B</span>
          <span class="icon-badge check">✓</span>
        </div>
        <span class="desc-tag">Measures are equal (degrees)</span>
      </div>

      
      <div class="card-item correct-card" data-cat="angle">
        <div class="card-header-row">
          <span class="math-expr">∠A ≅ ∠B</span>
          <span class="icon-badge check">✓</span>
        </div>
        <span class="desc-tag">Angles are congruent (shapes)</span>
      </div>
    </div>

    
    <div class="column">
      <div class="col-header incorrect">
        <span>✕</span>
        <span>Incorrect Notation</span>
      </div>

      
      <div class="card-item incorrect-card" data-cat="segment">
        <div class="card-header-row">
          <span class="math-expr"><span class="overbar">AB</span> = <span class="overbar">CD</span></span>
          <span class="icon-badge cross">✕</span>
        </div>
        <span class="desc-tag">Shapes cannot be equal</span>
      </div>

      
      <div class="card-item incorrect-card" data-cat="segment">
        <div class="card-header-row">
          <span class="math-expr">AB ≅ CD</span>
          <span class="icon-badge cross">✕</span>
        </div>
        <span class="desc-tag">Numbers cannot be congruent</span>
      </div>

      
      <div class="card-item incorrect-card" data-cat="angle">
        <div class="card-header-row">
          <span class="math-expr">m∠A ≅ m∠B</span>
          <span class="icon-badge cross">✕</span>
        </div>
        <span class="desc-tag">Degrees cannot be congruent</span>
      </div>

      
      <div class="card-item incorrect-card" data-cat="angle">
        <div class="card-header-row">
          <span class="math-expr">∠A = ∠B</span>
          <span class="icon-badge cross">✕</span>
        </div>
        <span class="desc-tag">Shapes cannot be equal</span>
      </div>
    </div>

  </div>

  <script>
    function filterCategory(cat, btn) {
      document.querySelectorAll('.filter-btn').forEach(b => b.classList.remove('active'));
      btn.classList.add('active');

      const cards = document.querySelectorAll('.card-item');
      cards.forEach(card => {
        if (cat === 'all' || card.getAttribute('data-cat') === cat) {
          card.style.display = 'flex';
        } else {
          card.style.display = 'none';
        }
      });
    }
  </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;
      color: #1e2945;
      background: #ffffff;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
      padding: 12px;
      gap: 12px;
    }

    .stepper-nav {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      width: 100%;
      max-width: 440px;
    }

    .step-btn {
      flex: 1;
      padding: 6px 10px;
      font-size: 13px;
      font-weight: 600;
      border-radius: 8px;
      border: 1px solid #e2e8f0;
      background: #f8fafc;
      color: #64748b;
      cursor: pointer;
      text-align: center;
      transition: all 0.25s ease;
    }

    .step-btn.active {
      background: #22b7ff;
      color: #ffffff;
      border-color: #22b7ff;
      box-shadow: 0 2px 6px rgba(34, 183, 255, 0.35);
    }

    .svg-container {
      width: 100%;
      max-width: 440px;
      aspect-ratio: 400 / 140;
    }

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

    /* SVG elements styling & transitions */
    .fade-elem {
      transition: opacity 0.35s ease, transform 0.35s ease;
    }

    .hidden {
      opacity: 0;
      pointer-events: none;
    }

    .visible {
      opacity: 1;
    }

    .cards-row {
      display: flex;
      flex-direction: column;
      gap: 8px;
      width: 100%;
      max-width: 440px;
    }

    .info-card {
      border: 1.5px solid #e2e8f0;
      border-radius: 10px;
      padding: 9px 12px;
      background: #f8fafc;
      transition: all 0.25s ease;
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: space-between;
    }

    .info-card.active {
      border-color: #22b7ff;
      background: #f0f9ff;
      box-shadow: 0 2px 8px rgba(34, 183, 255, 0.15);
    }

    .card-title {
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
    }

    .info-card.active .card-title {
      color: #0284c7;
    }

    .card-math {
      font-size: 15px;
      font-weight: 700;
      color: #1e2945;
      font-family: system-ui, sans-serif;
    }

    .overline {
      text-decoration: overline;
      margin-right: 2px;
    }
  </style>
</head>
<body>

  
  <div class="stepper-nav">
    <button class="step-btn active" id="btnStep1" onclick="setStep(1)">1. Total Segment</button>
    <button class="step-btn" id="btnStep2" onclick="setStep(2)">2. Equal Lengths</button>
    <button class="step-btn" id="btnStep3" onclick="setStep(3)">3. Congruence</button>
  </div>

  
  <div class="svg-container">
    <svg viewBox="0 0 400 140">
      <defs>
        
        <marker id="arrowL" viewBox="0 0 10 10" refX="1" refY="5" markerWidth="5" markerHeight="5" orient="auto">
          <path d="M 9 1 L 1 5 L 9 9" fill="none" stroke="#64748b" stroke-width="1.5" stroke-linecap="round"/>
        </marker>
        <marker id="arrowR" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="5" markerHeight="5" orient="auto">
          <path d="M 1 1 L 9 5 L 1 9" fill="none" stroke="#64748b" stroke-width="1.5" stroke-linecap="round"/>
        </marker>
      </defs>

      
      <g id="dimTotal" class="fade-elem visible">
        <line x1="50" y1="28" x2="350" y2="28" stroke="#94a3b8" stroke-width="1.5" stroke-dasharray="3 3" />
        <line x1="50" y1="20" x2="50" y2="36" stroke="#94a3b8" stroke-width="1.5" />
        <line x1="350" y1="20" x2="350" y2="36" stroke="#94a3b8" stroke-width="1.5" />
        <rect x="162" y="18" width="76" height="20" rx="4" fill="#ffffff" />
        <text x="200" y="33" text-anchor="middle" font-size="13" font-weight="700" fill="#475569">14 cm</text>
      </g>

      
      <line x1="50" y1="75" x2="350" y2="75" stroke="#1e2945" stroke-width="4" stroke-linecap="round" />

      
      <line id="segPM" class="fade-elem hidden" x1="50" y1="75" x2="200" y2="75" stroke="#22b7ff" stroke-width="4" stroke-linecap="round" />
      
      
      <line id="segMQ" class="fade-elem hidden" x1="200" y1="75" x2="350" y2="75" stroke="#0284c7" stroke-width="4" stroke-linecap="round" />

      
      <g id="tickMarks" class="fade-elem hidden">
        <line x1="125" y1="65" x2="125" y2="85" stroke="#0284c7" stroke-width="3" stroke-linecap="round" />
        <line x1="275" y1="65" x2="275" y2="85" stroke="#0284c7" stroke-width="3" stroke-linecap="round" />
      </g>

      
      <g id="labelsHalf" class="fade-elem hidden">
        <text x="125" y="105" text-anchor="middle" font-size="13" font-weight="700" fill="#0284c7">7 cm</text>
        <text x="275" y="105" text-anchor="middle" font-size="13" font-weight="700" fill="#0284c7">7 cm</text>
      </g>

      
      <circle cx="50" cy="75" r="5" fill="#1e2945" />
      <text x="50" y="105" text-anchor="middle" font-size="16" font-weight="700" fill="#1e2945">P</text>

      
      <g id="pointMGroup" class="fade-elem hidden">
        
        <circle cx="200" cy="75" r="11" fill="#22b7ff" fill-opacity="0.25" />
        <circle cx="200" cy="75" r="5.5" fill="#22b7ff" stroke="#ffffff" stroke-width="1.5" />
        <text x="200" y="105" text-anchor="middle" font-size="16" font-weight="800" fill="#0284c7">M</text>
        <text x="200" y="122" text-anchor="middle" font-size="11" font-weight="700" fill="#0284c7">MIDPOINT</text>
      </g>

      
      <circle cx="350" cy="75" r="5" fill="#1e2945" />
      <text x="350" y="105" text-anchor="middle" font-size="16" font-weight="700" fill="#1e2945">Q</text>
    </svg>
  </div>

  
  <div class="cards-row">
    <div class="info-card" id="card1" onclick="setStep(2)">
      <span class="card-title">1. Equal Lengths</span>
      <span class="card-math">PM = MQ = 7 cm</span>
    </div>

    <div class="info-card" id="card2" onclick="setStep(3)">
      <span class="card-title">2. Congruence Statement</span>
      <span class="card-math"><span class="overline">PM</span> ≅ <span class="overline">MQ</span></span>
    </div>
  </div>

  <script>
    let currentStep = 1;

    function setStep(step) {
      currentStep = step;

      // Nav buttons
      document.getElementById('btnStep1').classList.toggle('active', step === 1);
      document.getElementById('btnStep2').classList.toggle('active', step === 2);
      document.getElementById('btnStep3').classList.toggle('active', step === 3);

      // SVG Elements
      const pointMGroup = document.getElementById('pointMGroup');
      const tickMarks = document.getElementById('tickMarks');
      const labelsHalf = document.getElementById('labelsHalf');
      const segPM = document.getElementById('segPM');
      const segMQ = document.getElementById('segMQ');

      // Card Highlighting
      const card1 = document.getElementById('card1');
      const card2 = document.getElementById('card2');

      if (step === 1) {
        pointMGroup.classList.replace('visible', 'hidden');
        tickMarks.classList.replace('visible', 'hidden');
        labelsHalf.classList.replace('visible', 'hidden');
        segPM.classList.replace('visible', 'hidden');
        segMQ.classList.replace('visible', 'hidden');
        card1.classList.remove('active');
        card2.classList.remove('active');
      } else if (step === 2) {
        pointMGroup.classList.replace('hidden', 'visible');
        tickMarks.classList.replace('hidden', 'visible');
        labelsHalf.classList.replace('hidden', 'visible');
        segPM.classList.replace('hidden', 'visible');
        segMQ.classList.replace('hidden', 'visible');
        card1.classList.add('active');
        card2.classList.remove('active');
      } else if (step === 3) {
        pointMGroup.classList.replace('hidden', 'visible');
        tickMarks.classList.replace('hidden', 'visible');
        labelsHalf.classList.replace('hidden', 'visible');
        segPM.classList.replace('hidden', 'visible');
        segMQ.classList.replace('hidden', 'visible');
        card1.classList.remove('active');
        card2.classList.add('active');
      }
    }

    // Auto-advance with calm pedagogical pacing (can be manually clicked anytime)
    let timer = setInterval(() => {
      let next = currentStep >= 3 ? 1 : currentStep + 1;
      setStep(next);
    }, 4200);

    // Stop auto-timer on student click
    document.body.addEventListener('pointerdown', () => {
      if (timer) {
        clearInterval(timer);
        timer = null;
      }
    }, { once: true });
  </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: #1e293b;
      display: flex;
      flex-direction: column;
      align-items: center;
      padding: 8px 10px;
    }

    .main-container {
      width: 100%;
      max-width: 360px;
      display: flex;
      flex-direction: column;
      gap: 8px;
    }

    .controls-row {
      display: flex;
      gap: 6px;
      justify-content: space-between;
      align-items: center;
      width: 100%;
    }

    .btn-group {
      display: flex;
      background: #e2e8f0;
      padding: 3px;
      border-radius: 8px;
      gap: 2px;
    }

    .toggle-btn {
      background: transparent;
      border: none;
      outline: none;
      padding: 5px 9px;
      font-size: 12px;
      font-weight: 700;
      color: #1e293b;
      border-radius: 6px;
      cursor: pointer;
      transition: background 0.2s ease, color 0.2s ease, box-shadow 0.2s ease;
      white-space: nowrap;
    }

    .toggle-btn:hover {
      background: rgba(255, 255, 255, 0.6);
      color: #0f172a;
    }

    .toggle-btn.active {
      background: #2563eb;
      color: #ffffff;
      box-shadow: 0 1px 2px rgba(0,0,0,0.1);
    }

    .stage {
      position: relative;
      width: 100%;
      height: 180px;
      background: #ffffff;
      border-radius: 10px;
      box-shadow: inset 0 0 0 1px #cbd5e1;
      overflow: hidden;
      cursor: pointer;
    }

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

    .match-badge {
      position: absolute;
      bottom: 8px;
      left: 50%;
      transform: translateX(-50%) translateY(8px);
      background: #dbeafe;
      border: 1px solid #93c5fd;
      color: #1e40af;
      font-size: 12px;
      font-weight: 700;
      padding: 3px 10px;
      border-radius: 16px;
      opacity: 0;
      pointer-events: none;
      transition: opacity 0.3s ease, transform 0.3s ease;
      white-space: nowrap;
      box-shadow: 0 2px 4px rgba(0,0,0,0.05);
    }

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

    .moving-obj {
      transform-origin: 0 0;
      transition: transform 0.75s cubic-bezier(0.4, 0, 0.2, 1);
    }

    .actions-row {
      display: flex;
      gap: 8px;
      width: 100%;
    }

    .action-btn {
      flex: 1;
      background: #2563eb;
      color: #ffffff;
      border: none;
      border-radius: 7px;
      padding: 7px 12px;
      font-size: 13px;
      font-weight: 700;
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      transition: opacity 0.15s ease;
    }

    .action-btn:hover {
      opacity: 0.92;
    }

    .action-btn:active {
      opacity: 0.8;
    }

    .reset-btn {
      background: #e2e8f0;
      color: #0f172a;
      border: none;
      border-radius: 7px;
      padding: 7px 14px;
      font-size: 13px;
      font-weight: 700;
      cursor: pointer;
      transition: background 0.15s ease;
      white-space: nowrap;
    }

    .reset-btn:hover {
      background: #cbd5e1;
    }

    .reset-btn:active {
      opacity: 0.8;
    }

    .hint-label {
      text-align: center;
      font-size: 11px;
      font-weight: 600;
      color: #64748b;
    }
  </style>
</head>
<body>

  <div class="main-container">
    <div class="controls-row">
      
      <div class="btn-group">
        <button id="typeSegment" class="toggle-btn active" onclick="setType('segment')">Segment</button>
        <button id="typeAngle" class="toggle-btn" onclick="setType('angle')">Angle</button>
      </div>

      
      <div class="btn-group">
        <button id="btnTranslate" class="toggle-btn active" onclick="setMotion('translate')">Translate</button>
        <button id="btnRotate" class="toggle-btn" onclick="setMotion('rotate')">Rotate</button>
        <button id="btnReflect" class="toggle-btn" onclick="setMotion('reflect')">Reflect</button>
      </div>
    </div>

    <div class="stage" onclick="triggerMotion()" title="Click to transform">
      <svg viewBox="0 0 360 180" id="canvas">
        <defs>
          <pattern id="gridDots" width="18" height="18" patternUnits="userSpaceOnUse">
            <circle cx="9" cy="9" r="1" fill="#e2e8f0"/>
          </pattern>
        </defs>

        <rect width="100%" height="100%" fill="url(#gridDots)" />

        
        <text x="75" y="24" fill="#64748b" font-size="11" font-weight="700" text-anchor="middle">Source Object</text>
        <text x="265" y="24" fill="#64748b" font-size="11" font-weight="700" text-anchor="middle">Target Position</text>

        
        <g id="mirrorLine" style="display: none;">
          <line x1="170" y1="12" x2="170" y2="168" stroke="#94a3b8" stroke-width="1.5" stroke-dasharray="4 4"/>
          <text x="170" y="174" fill="#94a3b8" font-size="9" font-weight="700" text-anchor="middle">Mirror Axis</text>
        </g>

        
        <g id="targetGroup" stroke="#94a3b8" stroke-width="3" fill="none" stroke-dasharray="5 4" stroke-linecap="round" stroke-linejoin="round">
          
          <g id="targetSegment">
            <line x1="220" y1="95" x2="310" y2="95" />
            <line x1="265" y1="87" x2="265" y2="103" stroke="#94a3b8" stroke-width="2" stroke-dasharray="none"/>
            <circle cx="220" cy="95" r="3.5" fill="#94a3b8" stroke="none"/>
            <circle cx="310" cy="95" r="3.5" fill="#94a3b8" stroke="none"/>
          </g>

          
          <g id="targetAngle" style="display: none;">
            <polyline points="295,55 235,115 295,115" />
            <path d="M 260,115 A 25 25 0 0 0 252,98" stroke="#94a3b8" stroke-width="2" stroke-dasharray="none" />
            <line x1="254" y1="104" x2="260" y2="110" stroke="#94a3b8" stroke-width="2" stroke-dasharray="none"/>
            <circle cx="235" cy="115" r="3.5" fill="#94a3b8" stroke="none"/>
          </g>
        </g>

        
        <g id="movingObj" class="moving-obj">
          
          <g id="sourceSegment">
            <line x1="0" y1="0" x2="90" y2="0" stroke="#2563eb" stroke-width="3" stroke-linecap="round"/>
            <line x1="45" y1="-8" x2="45" y2="8" stroke="#2563eb" stroke-width="2"/>
            <circle cx="0" cy="0" r="3.5" fill="#2563eb"/>
            <circle cx="90" cy="0" r="3.5" fill="#2563eb"/>
          </g>

          
          <g id="sourceAngle" style="display: none;">
            <polyline points="60,-60 0,0 60,0" stroke="#2563eb" stroke-width="3" stroke-linecap="round" stroke-linejoin="round" fill="none"/>
            <path d="M 25,0 A 25 25 0 0 0 17,-17" stroke="#2563eb" stroke-width="2" fill="none"/>
            <line x1="19" y1="-11" x2="25" y2="-5" stroke="#2563eb" stroke-width="2"/>
            <circle cx="0" cy="0" r="3.5" fill="#2563eb"/>
          </g>
        </g>
      </svg>

      <div id="badge" class="match-badge">Exact Match: Congruent (≅)</div>
    </div>

    <div class="actions-row">
      <button id="btnAction" class="action-btn" onclick="triggerMotion()">
        <span id="actionLabel">Translate to Match ➔</span>
      </button>
      <button class="reset-btn" onclick="resetMotion()">Reset ↺</button>
    </div>

    <div class="hint-label">Click any motion or the diagram to animate</div>
  </div>

  <script>
    let currentType = 'segment';
    let currentMotion = 'translate';
    let isTransformed = false;
    let animTimeout = null;

    const configs = {
      segment: {
        translate: {
          start: { x: 30, y: 95, rot: 0, sx: 1 },
          target: { x: 220, y: 95, rot: 0, sx: 1 },
          label: 'Translate to Match ➔'
        },
        rotate: {
          start: { x: 60, y: 130, rot: -50, sx: 1 },
          target: { x: 220, y: 95, rot: 0, sx: 1 },
          label: 'Rotate to Match ➔'
        },
        reflect: {
          start: { x: 120, y: 95, rot: 0, sx: -1 },
          target: { x: 220, y: 95, rot: 0, sx: 1 },
          label: 'Reflect to Match ➔'
        }
      },
      angle: {
        translate: {
          start: { x: 45, y: 115, rot: 0, sx: 1 },
          target: { x: 235, y: 115, rot: 0, sx: 1 },
          label: 'Translate to Match ➔'
        },
        rotate: {
          start: { x: 75, y: 135, rot: -55, sx: 1 },
          target: { x: 235, y: 115, rot: 0, sx: 1 },
          label: 'Rotate to Match ➔'
        },
        reflect: {
          start: { x: 105, y: 115, rot: 0, sx: -1 },
          target: { x: 235, y: 115, rot: 0, sx: 1 },
          label: 'Reflect to Match ➔'
        }
      }
    };

    function updateView() {
      const isAngle = currentType === 'angle';
      document.getElementById('targetSegment').style.display = isAngle ? 'none' : 'block';
      document.getElementById('targetAngle').style.display = isAngle ? 'block' : 'none';
      document.getElementById('sourceSegment').style.display = isAngle ? 'none' : 'block';
      document.getElementById('sourceAngle').style.display = isAngle ? 'block' : 'none';
      document.getElementById('mirrorLine').style.display = currentMotion === 'reflect' ? 'block' : 'none';

      const cfg = configs[currentType][currentMotion];
      document.getElementById('actionLabel').textContent = cfg.label;

      resetMotion();
    }

    function setType(type) {
      currentType = type;
      document.getElementById('typeSegment').classList.toggle('active', type === 'segment');
      document.getElementById('typeAngle').classList.toggle('active', type === 'angle');
      updateView();
      // Auto-animate on mode switch for dynamic educational response
      setTimeout(triggerMotion, 60);
    }

    function setMotion(motion) {
      currentMotion = motion;
      document.getElementById('btnTranslate').classList.toggle('active', motion === 'translate');
      document.getElementById('btnRotate').classList.toggle('active', motion === 'rotate');
      document.getElementById('btnReflect').classList.toggle('active', motion === 'reflect');
      updateView();
      // Auto-animate on motion selection
      setTimeout(triggerMotion, 60);
    }

    function applyTransform(state) {
      const obj = document.getElementById('movingObj');
      obj.style.transform = `translate(${state.x}px, ${state.y}px) rotate(${state.rot}deg) scaleX(${state.sx})`;
    }

    function resetMotion() {
      if (animTimeout) clearTimeout(animTimeout);
      isTransformed = false;
      document.getElementById('badge').classList.remove('show');
      const cfg = configs[currentType][currentMotion];
      applyTransform(cfg.start);
    }

    function triggerMotion() {
      if (animTimeout) clearTimeout(animTimeout);

      if (isTransformed) {
        resetMotion();
        return;
      }

      isTransformed = true;
      const cfg = configs[currentType][currentMotion];
      applyTransform(cfg.target);

      animTimeout = setTimeout(() => {
        if (isTransformed) {
          document.getElementById('badge').classList.add('show');
        }
      }, 720);
    }

    // Initialize state
    updateView();
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
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    <span>AB = CD = 6 cm</span>
    <span>⟹</span>
    <span><span class="overline">AB</span> ≅ <span class="overline">CD</span></span>
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      1. Separate
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      2. Superimpose
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    Rigid motion maps <span class="overline">CD</span> directly onto <span class="overline">AB</span>.
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认识三角形：顶点、边、角与几何符号表示

三角形的分类：按角与按边的划分标准

三角形的高线：定义与锐角、直角、钝角三角形的高

三角形的中线：中点连线与等底同高面积平分

三角形的角平分线：内角平分线段及其特征

三角形的稳定性：力学原理与生活工程应用

综合辨析：高线、中线、角平分线的区别与位置特征

math

三角形的基础概念与重要线段

三角形三边关系：两边之和大于第三边的几何证明

三边关系应用：确定第三边的取值范围与拼摆判定

三角形内角和定理：辅助线添法与严格逻辑证明

角度计算：利用内角和与方程思想求解未知角

认识三角形的外角：定义、邻补角与外角个数

三角形外角定理：外角等于不相邻两内角和的推导

三角形的外角和：各顶点处一个外角和等于360°

综合推理：折叠、飞镖模型与凹四边形中的角度计算

三角形的边角关系与内角外角定理

Exterior Angle Theorem for Triangles

Proving the Triangle Inequality Theorem

Angle-Side Relationships and the Hinge Theorem

Classifying Acute, Right, and Obtuse Triangles Using Side Lengths

The Triangle Mid-Segment Theorem and Proof

Medians and the Centroid Theorem

Concurrency of Altitudes, Perpendicular Bisectors, and Angle Bisectors

Triangle Theorems and Deductive Properties

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

全等三角形的性质与判定（SSS、SAS、ASA、AAS）

Proving Triangle Congruence by SSS and SAS

Proving Triangle Congruence by ASA and AAS

Hypotenuse-Leg (HL) Congruence for Right Triangles

Using CPCTC in Multi-Step Geometric Proofs

Isosceles and Equilateral Triangle Theorems and Proofs

Proofs Involving Midpoints and Perpendicular Bisectors

Using Congruent Triangle Proofs in Problems

Triangle Congruence Criteria and Synthetic Proofs

角平分线的性质定理：角平分线上的点到两边距离相等

角平分线的判定定理：到角两边距离相等的点在角平分线上

三角形三条角平分线的交点（内心）：到三边距离相等

线段垂直平分线的性质定理：到线段两端距离相等

线段垂直平分线的判定定理：到两端距离相等的点在垂直平分线上

三角形三边垂直平分线的交点（外心）：到三顶点距离相等

综合应用：服务站选址与到点、到线距离最值问题

特殊线段的性质：角平分线与垂直平分线

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

三角形的重心：三条中线的交点与物理平衡中心

重心的性质：重心分每条中线为 2:1 的两段

尺规作图（一）：已知三边长作三角形（基于 SSS）

尺规作图（二）：已知两边及其夹角作三角形（基于 SAS）

尺规作图（三）：已知两角及其夹边作三角形（基于 ASA）

尺规作图（四）：已知底边及底边上的高线作等腰三角形

尺规作图（五）：已知一直角边和斜边作直角三角形（基于 HL）

三角形的重心与尺规作图专题

Semelhança de Triângulos

Congruência de Triângulos

Casos de Congruência: LAL, ALA e LLL

Transformações em Fractais

Transformações em Obras de Arte e Arquitetura

Semelhança, Congruência e Aplicações de Transformações

Cálculo de Área por Reconfiguração

Cálculo de Área por Aproximação de Cortes

Área de Figuras Compostas

Perímetro e Área: Relações e Aplicações

Relações Métricas em Triângulos Retângulos

Lei do Seno

Lei do Cosseno

Áreas e Relações Métricas em Triângulos

Razões Trigonométricas no Triângulo Retângulo

Seno, Cosseno e Tangente: Valores Notáveis

Resolvendo Problemas com Trigonometria no Triângulo

Ciclo Trigonométrico

Função Seno: Gráfico e Propriedades

Função Cosseno: Gráfico e Propriedades

Período e Amplitude de Funções Trigonométricas

Trigonometria: Razões e Funções

Fenômenos Periódicos: Ondas Sonoras

Fenômenos Periódicos: Fases da Lua

Fenômenos Periódicos: Movimentos Cíclicos

Modelagem de Fenômenos Periódicos Reais

Aplicação das Leis do Seno e do Cosseno

Problemas com Triângulos: Leis Trigonométricas

Comparando Representações de Fenômenos Periódicos

Aplicações da Trigonometria

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.10.GEO.2

Aligned learning resources

Related diagrams