<!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">
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      justify-content: center;
      min-height: 100vh;
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    .main-wrap {
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      max-width: 620px;
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      flex: 1 1 240px;
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      display: block;
      overflow: visible;
    }

    .tri {
      fill: #3b82f6;
      stroke: #1d4ed8;
      stroke-width: 1.5;
      transition: opacity 0.4s ease, fill 0.3s ease;
    }

    .area-c {
      fill: #f43f5e;
      stroke: #be123c;
      stroke-width: 1.5;
      transition: fill 0.3s ease;
    }

    .area-a, .area-b {
      fill: #f59e0b;
      stroke: #b45309;
      stroke-width: 1.5;
      transition: fill 0.3s ease;
    }

    .dim-tri .tri {
      opacity: 0.22;
    }

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      font-size: 15px;
      font-weight: 700;
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      text-anchor: middle;
      dominant-baseline: central;
      pointer-events: none;
      filter: drop-shadow(0 1px 2px rgba(0,0,0,0.3));
    }

    .lbl-dim {
      font-size: 11px;
      font-weight: 600;
      fill: #475569;
      text-anchor: middle;
      dominant-baseline: central;
      pointer-events: none;
    }

    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 10px;
      margin-top: 2px;
    }

    .btn {
      background: #ffffff;
      border: 1px solid #cbd5e1;
      color: #334155;
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      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      gap: 6px;
      box-shadow: 0 1px 2px rgba(0,0,0,0.05);
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    .btn.active {
      background: #2563eb;
      color: #ffffff;
      border-color: #1d4ed8;
      box-shadow: 0 2px 4px rgba(37,99,235,0.25);
    }

    .equation-bar {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      font-size: 16px;
      font-weight: 700;
      padding: 6px 16px;
      background: #ffffff;
      border-radius: 24px;
      border: 1px solid #e2e8f0;
      box-shadow: 0 1px 3px rgba(0,0,0,0.05);
    }

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      background: #ffe4e6;
      padding: 2px 8px;
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    }

    .tag-ab {
      color: #b45309;
      background: #fef3c7;
      padding: 2px 8px;
      border-radius: 6px;
    }

    .eq-symbol {
      color: #64748b;
    }
  </style>
</head>
<body>

<div class="main-wrap">
  
  <div class="diagrams-row" id="diagramContainer">
    
    
    <div class="square-card">
      <svg viewBox="-14 -14 228 228">
        
        <rect x="0" y="0" width="200" height="200" fill="#f1f5f9" stroke="#94a3b8" stroke-dasharray="3,3" stroke-width="1.5" rx="2" />
        
        
        <polygon class="area-c" points="135,0 200,135 65,200 0,65" />
        <text x="100" y="100" class="lbl-title">c²</text>

        
        <polygon class="tri" points="0,0 135,0 0,65" />
        <polygon class="tri" points="200,0 200,135 135,0" />
        <polygon class="tri" points="200,200 65,200 200,135" />
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        <text x="67" y="-7" class="lbl-dim">b</text>
        <text x="167" y="-7" class="lbl-dim">a</text>
        <text x="207" y="67" class="lbl-dim">b</text>
        <text x="207" y="167" class="lbl-dim">a</text>
      </svg>
    </div>

    
    <div class="square-card">
      <svg viewBox="-14 -14 228 228">
        
        <rect x="0" y="0" width="200" height="200" fill="#f1f5f9" stroke="#94a3b8" stroke-dasharray="3,3" stroke-width="1.5" rx="2" />

        
        <rect class="area-b" x="0" y="0" width="135" height="135" />
        <text x="67" y="67" class="lbl-title">b²</text>

        
        <rect class="area-a" x="135" y="135" width="65" height="65" />
        <text x="167" y="167" class="lbl-title">a²</text>

        
        
        <polygon class="tri" points="135,0 200,0 200,135" />
        <polygon class="tri" points="135,0 200,135 135,135" />
        
        
        <polygon class="tri" points="0,135 135,200 0,200" />
        <polygon class="tri" points="0,135 135,135 135,200" />

        
        <text x="67" y="-7" class="lbl-dim">b</text>
        <text x="167" y="-7" class="lbl-dim">a</text>
        <text x="207" y="67" class="lbl-dim">b</text>
        <text x="207" y="167" class="lbl-dim">a</text>
      </svg>
    </div>

  </div>

  
  <div class="controls">
    <button class="btn active" id="btnAll">All Pieces</button>
    <button class="btn" id="btnSub">− 4 Triangles</button>
  </div>

  
  <div class="equation-bar">
    <span class="tag-c">Area = c²</span>
    <span class="eq-symbol">=</span>
    <span class="tag-ab">a² + b²</span>
  </div>
</div>

<script>
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  const btnSub = document.getElementById('btnSub');
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    btnSub.classList.add('active');
    btnAll.classList.remove('active');
  }

  btnAll.addEventListener('click', showAll);
  btnSub.addEventListener('click', showSubtracted);
</script>

</body>
</html>

Geometric Dissection Proofs of the Pythagorean Theorem

<!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;
      user-select: none;
    }

    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: flex-start;
      padding: 12px;
      gap: 10px;
    }

    .diagram-wrap {
      width: 100%;
      max-width: 440px;
      display: flex;
      flex-direction: column;
      align-items: center;
    }

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

    .label-math {
      font-size: 15px;
      font-weight: 700;
      font-family: "Cambria Math", "Times New Roman", serif;
      font-style: italic;
    }

    .label-main {
      fill: #1e2945;
    }

    .label-blue {
      fill: #0369a1;
    }

    .label-purple {
      fill: #6d28d9;
    }

    /* Interactive controls */
    .controls {
      display: flex;
      gap: 8px;
      margin-top: 4px;
      flex-wrap: wrap;
      justify-content: center;
    }

    .step-btn {
      background: #f1f5f9;
      border: 1.5px solid transparent;
      color: #475569;
      font-size: 13px;
      font-weight: 600;
      padding: 6px 14px;
      border-radius: 20px;
      cursor: pointer;
      transition: all 0.25s ease;
    }

    .step-btn.active {
      background: #eff6ff;
      border-color: #22b7ff;
      color: #0284c7;
      box-shadow: 0 1px 4px rgba(34, 183, 255, 0.2);
    }

    .math-card {
      width: 100%;
      max-width: 400px;
      min-height: 48px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      display: flex;
      align-items: center;
      justify-content: center;
      padding: 6px 12px;
      text-align: center;
      font-size: 15px;
      font-weight: 600;
    }

    .formula {
      font-family: "Cambria Math", "Times New Roman", serif;
      font-size: 17px;
      letter-spacing: 0.5px;
    }

    .c-blue { color: #0284c7; }
    .c-purple { color: #7c3aed; }
    .c-dark { color: #0f172a; }
  </style>
</head>
<body>

  <div class="diagram-wrap">
    <svg viewBox="0 0 430 330" aria-label="Garfield's Pythagorean Proof Diagram">
      <defs>
        
        <linearGradient id="blueGrad" x1="0%" y1="0%" x2="100%" y2="100%">
          <stop offset="0%" stop-color="#e0f2fe"/>
          <stop offset="100%" stop-color="#bae6fd"/>
        </linearGradient>

        
        <linearGradient id="purpleGrad" x1="0%" y1="0%" x2="100%" y2="100%">
          <stop offset="0%" stop-color="#f5f3ff"/>
          <stop offset="100%" stop-color="#ddd6fe"/>
        </linearGradient>
      </defs>

      
      
      <path d="M 52 24 L 40 24 L 40 160 L 32 160 L 40 160 L 40 296 L 52 296" 
            fill="none" stroke="#94a3b8" stroke-width="1.8" stroke-linecap="round" stroke-linejoin="round"/>
      <text x="24" y="165" text-anchor="middle" class="label-math label-main" font-size="16">a + b</text>

      
      
      <line x1="68" y1="24" x2="68" y2="176" stroke="#cbd5e1" stroke-width="1.5" stroke-dasharray="3,3"/>
      <path d="M 64 24 L 72 24 M 64 176 L 72 176" stroke="#94a3b8" stroke-width="1.5"/>
      <text x="60" y="105" text-anchor="end" class="label-math label-blue">b</text>

      
      <line x1="68" y1="176" x2="68" y2="296" stroke="#cbd5e1" stroke-width="1.5" stroke-dasharray="3,3"/>
      <path d="M 64 296 L 72 296" stroke="#94a3b8" stroke-width="1.5"/>
      <text x="60" y="242" text-anchor="end" class="label-math label-blue">a</text>

      
      
      <polygon id="triMid" points="80,176 200,24 248,296" 
               fill="url(#purpleGrad)" stroke="#7c3aed" stroke-width="2.5" stroke-linejoin="round"/>

      
      
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               fill="url(#blueGrad)" stroke="#0284c7" stroke-width="2.5" stroke-linejoin="round"/>

      
      
      <polygon id="triBot" points="80,176 248,296 80,296" 
               fill="url(#blueGrad)" stroke="#0284c7" stroke-width="2.5" stroke-linejoin="round"/>

      
      
      <path d="M 80 40 L 96 40 L 96 24" fill="none" stroke="#0284c7" stroke-width="1.8"/>

      
      <path d="M 80 280 L 96 280 L 96 296" fill="none" stroke="#0284c7" stroke-width="1.8"/>

      
      
      
      <path d="M 90 163 L 103 173 L 93 186" fill="none" stroke="#7c3aed" stroke-width="2"/>
      <circle cx="95" cy="174" r="1.5" fill="#7c3aed"/>

      
      
      <text x="140" y="16" text-anchor="middle" class="label-math label-blue">a</text>

      
      <text x="164" y="316" text-anchor="middle" class="label-math label-blue">b</text>

      
      <text x="148" y="93" text-anchor="middle" class="label-math label-purple">c</text>
      <text x="172" y="240" text-anchor="middle" class="label-math label-purple">c</text>

      
      <text x="116" y="74" text-anchor="middle" font-size="12" font-weight="600" fill="#0369a1">½ab</text>
      <text x="132" y="266" text-anchor="middle" font-size="12" font-weight="600" fill="#0369a1">½ab</text>
      <text x="176" y="165" text-anchor="middle" font-size="14" font-weight="700" fill="#6d28d9">½c²</text>
    </svg>

    
    <div class="controls">
      <button class="step-btn active" onclick="setStep(0)">1. Trapezoid</button>
      <button class="step-btn" onclick="setStep(1)">2. Three Triangles</button>
      <button class="step-btn" onclick="setStep(2)">3. Result</button>
    </div>

    
    <div class="math-card">
      <div id="mathText" class="formula">
        <span class="c-dark">Area</span> = <span class="c-dark">½ (a + b)(a + b)</span>
      </div>
    </div>
  </div>

  <script>
    const steps = [
      {
        text: '<span class="c-dark">Trapezoid Area</span> = <span class="c-dark">½(a + b)²</span> = <span class="c-dark">½(a² + 2ab + b²)</span>',
        hi: 'all'
      },
      {
        text: '<span class="c-dark">3 Triangles Area</span> = <span class="c-blue">½ab</span> + <span class="c-blue">½ab</span> + <span class="c-purple">½c²</span> = <span class="c-blue">ab</span> + <span class="c-purple">½c²</span>',
        hi: 'triangles'
      },
      {
        text: '<span class="c-dark">½(a² + 2ab + b²)</span> = <span class="c-dark">ab + ½c²</span> &nbsp;➔&nbsp; <strong class="c-dark" style="font-size:18px;">a² + b² = c²</strong>',
        hi: 'result'
      }
    ];

    function setStep(idx) {
      document.querySelectorAll('.step-btn').forEach((btn, i) => {
        btn.classList.toggle('active', i === idx);
      });

      const card = document.getElementById('mathText');
      card.innerHTML = steps[idx].text;

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      const bot = document.getElementById('triBot');
      const mid = document.getElementById('triMid');

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        bot.style.opacity = '0.9';
        mid.style.opacity = '0.9';
      } else if (idx === 1) {
        top.style.opacity = '1';
        bot.style.opacity = '1';
        mid.style.opacity = '1';
      } else {
        top.style.opacity = '1';
        bot.style.opacity = '1';
        mid.style.opacity = '1';
      }
    }
  </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: #ffffff;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 12px;
      user-select: none;
    }

    .header-pill {
      display: inline-flex;
      align-items: center;
      gap: 6px;
      font-size: 13px;
      font-weight: 700;
      color: #0284c7;
      background: #e0f2fe;
      padding: 4px 12px;
      border-radius: 999px;
    }

    .svg-container {
      width: 100%;
      max-width: 520px;
      aspect-ratio: 520 / 300;
      position: relative;
    }

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

    .label {
      font-size: 13px;
      font-weight: 600;
      text-anchor: middle;
      dominant-baseline: central;
    }

    .math-bar {
      width: 100%;
      max-width: 500px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 8px 12px;
      display: flex;
      align-items: center;
      justify-content: space-around;
      font-size: 14px;
      font-weight: 700;
      gap: 6px;
      flex-wrap: wrap;
    }

    .math-item {
      display: flex;
      align-items: center;
      gap: 4px;
      padding: 4px 8px;
      border-radius: 8px;
      transition: background 0.2s, box-shadow 0.2s;
    }
    .math-item.active {
      background: #ffffff;
      box-shadow: 0 2px 6px rgba(0,0,0,0.08);
    }

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      display: flex;
      gap: 8px;
      margin-top: 4px;
    }

    .step-btn {
      border: 1px solid #cbd5e1;
      background: #ffffff;
      color: #475569;
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      border-radius: 8px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      gap: 6px;
      transition: all 0.2s;
    }
    .step-btn:hover {
      background: #f1f5f9;
      color: #0f172a;
    }
    .step-btn.active {
      background: #0284c7;
      border-color: #0284c7;
      color: #ffffff;
    }

    /* Angle arcs */
    .arc-alpha { stroke: #2563eb; fill: rgba(37, 99, 235, 0.18); stroke-width: 2; }
    .arc-beta  { stroke: #d97706; fill: rgba(217, 119, 6, 0.18); stroke-width: 2; }
    .arc-theta { stroke: #16a34a; fill: rgba(22, 163, 74, 0.22); stroke-width: 2; }
    .arc-straight { stroke: #94a3b8; stroke-dasharray: 4 4; fill: none; stroke-width: 1.5; }

    .highlight-theta {
      filter: drop-shadow(0 0 6px rgba(22, 163, 74, 0.5));
    }
  </style>
</head>
<body>

  <div class="header-pill">Garfield's Proof: Proving &theta; = 90&deg;</div>

  <div class="svg-container">
    <svg viewBox="0 0 520 290">
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          <stop offset="0%" stop-color="#4ade80" stop-opacity="0.3"/>
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      </defs>

      
      
      
      
      
      

      
      <polygon id="tri1" points="40,230 40,90 240,230" fill="url(#t1Grad)" stroke="#0284c7" stroke-width="2"/>
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      <line x1="40" y1="90" x2="460" y2="30" stroke="#94a3b8" stroke-width="1.5" stroke-dasharray="4 4"/>

      
      <path d="M 40 106 L 56 106 L 56 90" fill="none" stroke="#0284c7" stroke-width="1.5" />
      <path d="M 460 214 L 444 214 L 444 230" fill="none" stroke="#d97706" stroke-width="1.5" />

      
      <text class="label" x="25" y="160" fill="#0284c7">b</text>
      <text class="label" x="140" y="248" fill="#0284c7">a</text>
      <text class="label" x="130" y="145" fill="#0284c7" font-weight="700">c</text>

      <text class="label" x="350" y="248" fill="#d97706">b</text>
      <text class="label" x="478" y="130" fill="#d97706">a</text>
      <text class="label" x="365" y="115" fill="#d97706" font-weight="700">c</text>

      
      <line x1="20" y1="230" x2="480" y2="230" stroke="#334155" stroke-width="3" stroke-linecap="round"/>
      <circle cx="240" cy="230" r="4.5" fill="#1e2945"/>

      
      <path id="arc180" d="M 160 230 A 80 80 0 0 1 320 230" class="arc-straight"/>
      <text id="lbl180" class="label" x="240" y="135" fill="#64748b" font-size="12px">180&deg; straight line</text>

      
      
      
      
      <path id="pathAlpha" d="M 190 230 A 50 50 0 0 0 199 201.3 L 240 230 Z" class="arc-alpha"/>
      <text class="label" x="195" y="218" fill="#1d4ed8" font-weight="700">&alpha;</text>

      
      
      <path id="pathBeta" d="M 240 230 L 277 196.4 A 50 50 0 0 0 290 230 Z" class="arc-beta"/>
      <text class="label" x="282" y="218" fill="#b45309" font-weight="700">&beta;</text>

      
      <path id="pathTheta" d="M 240 230 L 199 201.3 A 50 50 0 0 1 277 196.4 Z" class="arc-theta"/>
      
      <g id="thetaRightBox" opacity="0">
        <path d="M 223.6 218.5 L 212.1 202.4 L 228.5 190.9" fill="none" stroke="#16a34a" stroke-width="2"/>
      </g>
      <text id="lblTheta" class="label" x="240" y="180" fill="#15803d" font-weight="800" font-size="16px">&theta;</text>

      
      <path d="M 40 120 A 30 30 0 0 0 64.6 107.2 L 40 90 Z" fill="rgba(217, 119, 6, 0.18)" stroke="#d97706" stroke-width="1.5"/>
      <text class="label" x="54" y="125" fill="#b45309" font-size="11px">&beta;</text>

      
      <path d="M 438 49.9 A 30 30 0 0 0 460 60 L 460 30 Z" fill="rgba(37, 99, 235, 0.18)" stroke="#2563eb" stroke-width="1.5"/>
      <text class="label" x="444" y="66" fill="#1d4ed8" font-size="11px">&alpha;</text>

    </svg>
  </div>

  <div class="math-bar">
    <div class="math-item" id="m1" style="color:#0284c7;">&alpha; + &beta; = 90&deg;</div>
    <span style="color:#94a3b8;">&bull;</span>
    <div class="math-item" id="m2" style="color:#64748b;">Line = 180&deg;</div>
    <span style="color:#94a3b8;">&bull;</span>
    <div class="math-item" id="m3" style="color:#16a34a;">&theta; = 180&deg; &minus; 90&deg; = 90&deg;</div>
  </div>

  <div class="btn-row">
    <button class="step-btn active" id="btn1" onclick="setStep(0)">1. Angles &alpha; &amp; &beta;</button>
    <button class="step-btn" id="btn2" onclick="setStep(1)">2. Straight Line</button>
    <button class="step-btn" id="btn3" onclick="setStep(2)">3. &theta; is Right Angle</button>
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        btn: 'btn1',
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    setStep(0);
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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">
  <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;
      color: #1e2945;
      background: #ffffff;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 12px 16px;
      user-select: none;
    }

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

    .pill-btn {
      appearance: none;
      border: 1px solid #e2e8f0;
      background: #f8fafc;
      color: #64748b;
      font-size: 13px;
      font-weight: 600;
      padding: 6px 14px;
      border-radius: 20px;
      cursor: pointer;
      transition: all 0.2s ease;
    }

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

    .pill-btn.active-legs {
      background: #eff6ff;
      color: #2563eb;
      border-color: #93c5fd;
      box-shadow: 0 0 0 1px #2563eb;
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    .pill-btn.active-hyp {
      background: #fff1f2;
      color: #f43f5e;
      border-color: #fda4af;
      box-shadow: 0 0 0 1px #f43f5e;
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    .pill-btn.active-area {
      background: #f0fdf4;
      color: #16a34a;
      border-color: #86efac;
      box-shadow: 0 0 0 1px #16a34a;
    }

    .diagram-area {
      width: 100%;
      max-width: 380px;
      height: 230px;
      display: flex;
      align-items: center;
      justify-content: center;
    }

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

    .side-leg {
      stroke: #2563eb;
      stroke-width: 4;
      stroke-linecap: round;
      transition: stroke-width 0.25s ease, opacity 0.25s ease;
      cursor: pointer;
    }

    .side-hyp {
      stroke: #f43f5e;
      stroke-width: 4;
      stroke-linecap: round;
      transition: stroke-width 0.25s ease, opacity 0.25s ease;
      cursor: pointer;
    }

    .triangle-fill {
      fill: #f8fafc;
      transition: fill 0.25s ease;
      cursor: pointer;
    }

    .rect-ghost {
      fill: none;
      stroke: #cbd5e1;
      stroke-dasharray: 5 4;
      stroke-width: 1.5;
      opacity: 0;
      transition: opacity 0.3s ease;
    }

    .rect-ghost.visible {
      opacity: 1;
    }

    .right-angle {
      fill: none;
      stroke: #94a3b8;
      stroke-width: 2;
    }

    .label-text {
      font-size: 16px;
      font-weight: 700;
      font-style: italic;
      font-family: "Times New Roman", Times, serif;
      text-anchor: middle;
      dominant-baseline: central;
      transition: transform 0.2s ease, opacity 0.2s ease;
      cursor: pointer;
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    .label-a, .label-b { fill: #2563eb; }
    .label-c { fill: #f43f5e; }

    .tag-text {
      font-size: 11px;
      font-weight: 700;
      font-style: normal;
      font-family: system-ui, sans-serif;
      text-anchor: middle;
      opacity: 0;
      transition: opacity 0.25s ease;
    }

    .dimmed {
      opacity: 0.25 !important;
    }

    .focused {
      stroke-width: 6 !important;
      opacity: 1 !important;
    }

    .formula-card {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 8px 18px;
      font-size: 17px;
      font-family: "Times New Roman", Times, serif;
      font-style: italic;
      font-weight: 600;
    }

    .math-sym {
      font-style: normal;
      color: #64748b;
    }

    .math-leg {
      color: #2563eb;
      font-weight: 700;
    }

    .math-hyp {
      color: #f43f5e;
      font-weight: 700;
    }
  </style>
</head>
<body>

  <div class="toolbar">
    <button class="pill-btn active-all" id="btn-all" onclick="setMode('all')">All</button>
    <button class="pill-btn" id="btn-legs" onclick="setMode('legs')">Legs (<span style="font-family:serif;font-style:italic">a, b</span>)</button>
    <button class="pill-btn" id="btn-hyp" onclick="setMode('hyp')">Hypotenuse (<span style="font-family:serif;font-style:italic">c</span>)</button>
    <button class="pill-btn" id="btn-area" onclick="setMode('area')">Area (½<span style="font-family:serif;font-style:italic">ab</span>)</button>
  </div>

  <div class="diagram-area">
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      <polygon id="ghostRect" class="rect-ghost" points="70,40 270,40 270,190" />

      
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      <line id="legB" class="side-leg" x1="70" y1="190" x2="270" y2="190" onclick="setMode('legs')" />
      <line id="hypC" class="side-hyp" x1="70" y1="40" x2="270" y2="190" onclick="setMode('hyp')" />

      
      <text id="lblA" class="label-text label-a" x="50" y="115" onclick="setMode('legs')">a</text>
      <text id="lblB" class="label-text label-b" x="170" y="210" onclick="setMode('legs')">b</text>
      <text id="lblC" class="label-text label-c" x="180" y="105" onclick="setMode('hyp')">c</text>

      
      <text id="tagLegsA" class="tag-text label-a" x="38" y="95">LEG</text>
      <text id="tagLegsB" class="tag-text label-b" x="170" y="224">LEG</text>
      <text id="tagHyp" class="tag-text label-c" x="195" y="90">HYPOTENUSE</text>
      <text id="tagArea" class="tag-text" fill="#16a34a" x="135" y="145">½ · (a × b)</text>
    </svg>
  </div>

  <div class="formula-card">
    <span style="color:#1e2945;font-style:normal;font-weight:700">Area</span>
    <span class="math-sym">=</span>
    <span>½</span>
    <span class="math-sym">·</span>
    <span class="math-leg">a</span>
    <span class="math-sym">·</span>
    <span class="math-leg">b</span>
  </div>

  <script>
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      // Buttons
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        const btn = document.getElementById('btn-' + m);
        btn.className = 'pill-btn' + (m === mode ? ' active-' + m : '');
      });

      // Elements
      const legA = document.getElementById('legA');
      const legB = document.getElementById('legB');
      const hypC = document.getElementById('hypC');
      const lblA = document.getElementById('lblA');
      const lblB = document.getElementById('lblB');
      const lblC = document.getElementById('lblC');
      const tagA = document.getElementById('tagLegsA');
      const tagB = document.getElementById('tagLegsB');
      const tagH = document.getElementById('tagHyp');
      const tagArea = document.getElementById('tagArea');
      const ghostRect = document.getElementById('ghostRect');
      const triBody = document.getElementById('triBody');

      // Reset
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        legA.classList.add('focused');
        legB.classList.add('focused');
        hypC.classList.add('dimmed');
        lblC.classList.add('dimmed');
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        hypC.classList.add('focused');
        legA.classList.add('dimmed');
        legB.classList.add('dimmed');
        lblA.classList.add('dimmed');
        lblB.classList.add('dimmed');
        tagH.style.opacity = '1';
      } else if (mode === 'area') {
        ghostRect.classList.add('visible');
        triBody.style.fill = '#dcfce7';
        tagArea.style.opacity = '1';
      }
    }
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
      background: #ffffff;
      color: #1e293b;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      padding: 10px 12px 14px;
      min-height: 100%;
      user-select: none;
    }

    /* SVG Diagram */
    .svg-container {
      width: 100%;
      max-width: 310px;
      display: flex;
      justify-content: center;
    }
    svg {
      width: 100%;
      height: auto;
      overflow: visible;
      cursor: pointer;
    }

    /* Interactive Shapes */
    .triangle-poly {
      fill: #bae6fd;
      stroke: #0284c7;
      stroke-width: 2;
      transition: fill 0.25s ease, opacity 0.25s ease, stroke 0.25s ease;
    }
    .inner-square-poly {
      fill: #fef08a;
      stroke: #d97706;
      stroke-width: 2;
      transition: fill 0.25s ease, opacity 0.25s ease, stroke 0.25s ease;
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    .outer-boundary {
      fill: none;
      stroke: #0f172a;
      stroke-width: 2.5;
      stroke-dasharray: none;
      transition: opacity 0.25s ease, stroke 0.25s ease, stroke-width 0.25s ease;
    }
    .right-angle-marker {
      stroke: #0284c7;
      stroke-width: 1.5;
      fill: none;
      transition: opacity 0.25s ease;
    }

    /* State Dimming */
    .dimmed { opacity: 0.18 !important; }
    .spotlight-tri .triangle-poly { fill: #7dd3fc; stroke: #0369a1; stroke-width: 2.5; }
    .spotlight-inner .inner-square-poly { fill: #fde047; stroke: #b45309; stroke-width: 2.5; }
    .spotlight-outer .outer-boundary { stroke: #2563eb; stroke-width: 3.5; }

    /* SVG Text */
    .lbl {
      font-size: 13px;
      font-weight: 700;
      text-anchor: middle;
      dominant-baseline: central;
      font-family: 'Times New Roman', serif;
      font-style: italic;
      pointer-events: none;
      transition: opacity 0.25s ease;
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    .lbl-c { fill: #0f172a; }
    .lbl-leg { fill: #0369a1; }
    .lbl-inner { fill: #b45309; font-size: 12px; font-weight: 800; font-family: system-ui, sans-serif; font-style: normal; }

    /* Buttons */
    .controls {
      display: grid;
      grid-template-columns: repeat(3, 1fr);
      gap: 6px;
      width: 100%;
      max-width: 340px;
      margin: 6px 0;
    }
    .btn-toggle {
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      padding: 6px 4px;
      border-radius: 8px;
      border: 1.5px solid #e2e8f0;
      background: #f8fafc;
      color: #334155;
      cursor: pointer;
      font-size: 11px;
      font-weight: 700;
      line-height: 1.25;
      transition: all 0.2s ease;
    }
    .btn-toggle .formula {
      font-size: 10px;
      font-weight: 600;
      opacity: 0.85;
      margin-top: 2px;
    }
    .btn-toggle:hover {
      background: #f1f5f9;
      border-color: #cbd5e1;
    }
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      background: #f1f5f9;
      border-color: #0f172a;
      color: #0f172a;
      box-shadow: 0 0 0 1px #0f172a;
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      background: #e0f2fe;
      border-color: #0284c7;
      color: #0369a1;
      box-shadow: 0 0 0 1px #0284c7;
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      background: #fef9c3;
      border-color: #d97706;
      color: #b45309;
      box-shadow: 0 0 0 1px #d97706;
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    /* Equation Card */
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      width: 100%;
      max-width: 340px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      padding: 8px 10px;
      text-align: center;
      font-size: 13px;
      font-weight: 600;
      line-height: 1.4;
      display: flex;
      flex-direction: column;
      gap: 3px;
    }
    .eq-row {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 4px;
      flex-wrap: wrap;
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    .term {
      padding: 1px 4px;
      border-radius: 4px;
      transition: all 0.2s ease;
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    .term-c { color: #0f172a; }
    .term-tri { color: #0284c7; }
    .term-inner { color: #d97706; }
    .term-res { color: #16a34a; font-weight: 700; }

    .hl-outer { background: #e2e8f0; font-weight: 800; }
    .hl-tri { background: #bae6fd; font-weight: 800; }
    .hl-inner { background: #fef08a; font-weight: 800; }
  </style>
</head>
<body>

  
  <div class="svg-container">
    <svg id="diagram" viewBox="0 0 340 300">
      
      <g id="grp-triangles">
        
        <polygon class="triangle-poly" points="60,260 280,260 139.2,154.4" />
        
        <polygon class="triangle-poly" points="280,260 280,40 174.4,180.8" />
        
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        <polygon class="triangle-poly" points="60,40 60,260 165.6,119.2" />

        
        <path class="right-angle-marker" d="M 133.2 162.4 L 141.2 168.4 L 147.2 160.4" />
        <path class="right-angle-marker" d="M 182.4 186.8 L 188.4 178.8 L 180.4 172.8" />
        <path class="right-angle-marker" d="M 206.8 137.6 L 198.8 131.6 L 192.8 139.6" />
        <path class="right-angle-marker" d="M 157.6 113.2 L 151.6 121.2 L 159.6 127.2" />

        
        <text class="lbl lbl-leg" x="90" y="214">a</text>
        <text class="lbl lbl-leg" x="216" y="214">b</text>
        <text class="lbl lbl-leg" x="238" y="230">a</text>
        <text class="lbl lbl-leg" x="238" y="96">b</text>
        <text class="lbl lbl-leg" x="250" y="86">a</text>
        <text class="lbl lbl-leg" x="124" y="86">b</text>
        <text class="lbl lbl-leg" x="102" y="70">a</text>
        <text class="lbl lbl-leg" x="102" y="204">b</text>
      </g>

      
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        <polygon class="inner-square-poly" points="139.2,154.4 174.4,180.8 200.8,145.6 165.6,119.2" />
        <text class="lbl lbl-inner" x="170" y="150">b − a</text>
      </g>

      
      <g id="grp-outer">
        <rect class="outer-boundary" x="60" y="40" width="220" height="220" />
        
        <text class="lbl lbl-c" x="170" y="278">c</text>
        <text class="lbl lbl-c" x="170" y="22">c</text>
        <text class="lbl lbl-c" x="42" y="150">c</text>
        <text class="lbl lbl-c" x="298" y="150">c</text>
      </g>
    </svg>
  </div>

  
  <div class="controls">
    <button class="btn-toggle" id="btn-outer">
      <span>Outer Square</span>
      <span class="formula">Area = c²</span>
    </button>
    <button class="btn-toggle" id="btn-tri">
      <span>4 Triangles</span>
      <span class="formula">4 × (½ab) = 2ab</span>
    </button>
    <button class="btn-toggle" id="btn-inner">
      <span>Inner Square</span>
      <span class="formula">Area = (b − a)²</span>
    </button>
  </div>

  
  <div class="eq-box">
    <div class="eq-row">
      <span class="term term-c" id="t-c2">c²</span>
      <span>=</span>
      <span class="term term-tri" id="t-tri1">4(½ab)</span>
      <span>+</span>
      <span class="term term-inner" id="t-in1">(b − a)²</span>
    </div>
    <div class="eq-row">
      <span>=</span>
      <span class="term term-tri" id="t-tri2">2ab</span>
      <span>+</span>
      <span class="term term-inner" id="t-in2">(b² − 2ab + a²)</span>
      <span>=</span>
      <span class="term term-res" id="t-res">a² + b²</span>
    </div>
  </div>

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    const grpOuter = document.getElementById('grp-outer');
    const grpTri = document.getElementById('grp-triangles');
    const grpInner = document.getElementById('grp-inner');

    const btnOuter = document.getElementById('btn-outer');
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    const btnInner = document.getElementById('btn-inner');

    const tC2 = document.getElementById('t-c2');
    const tTri1 = document.getElementById('t-tri1');
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        btnInner.classList.add('active-inner');
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        tIn2.classList.add('hl-inner');
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    }

    // Button clicks
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    btnTri.addEventListener('click', () => setMode('triangles'));
    btnInner.addEventListener('click', () => setMode('inner'));

    // SVG component clicks
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Conjuntos numéricos: de los naturales a los reales

Identificación de números irracionales en la vida cotidiana

Expansión decimal periódica y no periódica

Conversión de decimal periódico a fracción generatriz

Representación geométrica de raíces en la recta real

Densidad y completitud de los números reales

math

Estructura y clasificación de los números reales

勾股定理的几何发现与赵爽弦图面积证明

勾股定理的基础计算：已知两边求第三边与勾股数

勾股定理的逆定理：如果 a²+b²=c² 则三角形是直角三角形

勾股定理与折叠问题：设未知数建立一元二次方程求解

平面距离与数轴表示：勾股定理在数轴上画出无理数线段

立体图形表面最短路径：“蚂蚁爬行”与圆柱、长方体展开图

综合应用：水深与芦苇问题、梯子下滑及航海方位角测距

勾股定理及其逆定理与综合应用

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

Right-Angled Triangles and Introduction to Pythagoras Theorem

Finding the Hypotenuse Using Pythagoras

Finding a Shorter Side Using Pythagoras

Pythagoras' Theorem in Real-World Problems

Pythagorean Triples and Patterns

Verifying Pythagoras' Theorem with Digital Tools

Pythagoras' Theorem

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.8

Aligned learning resources

Related diagrams