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# Why Triangles? Let's start with a simple triangle: <svg width="200" height="180" viewBox="0 0 200 180" xmlns="http://www.w3.org/2000/svg"> <polygon points="50,150 150,150 100,30" fill="#6fa8dc" stroke="#054a91" stroke-width="4" /> <text x="40" y="160" font-size="18" fill="#054a91">A</text> <text x="160" y="160" font-size="18" fill="#054a91">B</text> <text x="95" y="20" font-size="18" fill="#054a91">C</text> </svg> Triangles have three sides and three angles.
## Triangles are Simple and Stable Why does simplicity matter? <svg width="300" height="150" viewBox="0 0 300 150" xmlns="http://www.w3.org/2000/svg"> <polygon points="50,130 150,20 250,130" fill="#f9cb9c" stroke="#a85c00" stroke-width="3" /> <text x="45" y="140" font-size="16" fill="#a85c00">Vertex 1</text> <text x="150" y="10" font-size="16" fill="#a85c00" text-anchor="middle">Vertex 2</text> <text x="255" y="140" font-size="16" fill="#a85c00">Vertex 3</text> </svg> Try pushing a triangle shape made from sticks — it won’t change shape easily!
## Triangles Provide Strength Look at this bridge structure: <svg width="350" height="150" viewBox="0 0 350 150" xmlns="http://www.w3.org/2000/svg"> <line x1="20" y1="130" x2="330" y2="130" stroke="#444" stroke-width="6" /> <line x1="20" y1="130" x2="100" y2="40" stroke="#0b5394" stroke-width="4" /> <line x1="100" y1="40" x2="180" y2="130" stroke="#0b5394" stroke-width="4" /> <line x1="180" y1="130" x2="260" y2="40" stroke="#0b5394" stroke-width="4" /> <line x1="260" y1="40" x2="330" y2="130" stroke="#0b5394" stroke-width="4" /> <circle cx="100" cy="40" r="5" fill="#0b5394" /> <circle cx="180" cy="130" r="5" fill="#0b5394" /> <circle cx="260" cy="40" r="5" fill="#0b5394" /> </svg> The triangles prevent the bridge from collapsing under pressure.
## Try This! What do you think? <svg width="300" height="150" viewBox="0 0 300 150" xmlns="http://www.w3.org/2000/svg"> <rect x="50" y="40" width="80" height="80" fill="#d9d9d9" stroke="#666" stroke-width="3" /> <rect x="150" y="40" width="80" height="80" fill="#d9d9d9" stroke="#666" stroke-width="3" /> </svg> <div class="fragment"> Squares can lose shape easily unless they have internal supports. </div>
## Triangles are the Building Blocks Because of their rigidity, triangles form the foundation of many structures. <svg width="200" height="180" viewBox="0 0 200 180" xmlns="http://www.w3.org/2000/svg"> <polygon points="50,150 150,150 100,30" fill="#6fa8dc" stroke="#054a91" stroke-width="4" /> <line x1="50" y1="150" x2="100" y2="30" stroke="#054a91" stroke-width="2" /> <line x1="150" y1="150" x2="100" y2="30" stroke="#054a91" stroke-width="2" /> <text x="40" y="160" font-size="18" fill="#054a91">A</text> <text x="160" y="160" font-size="18" fill="#054a91">B</text> <text x="95" y="20" font-size="18" fill="#054a91">C</text> </svg>
## Types of Triangles - Equilateral: all sides equal - Isosceles: two sides equal - Scalene: all sides different <svg width="600" height="180" xmlns="http://www.w3.org/2000/svg"> <!-- Equilateral --> <polygon points="50,130 110,130 80,70" fill="#ffd966" stroke="#b57f00" stroke-width="3" /> <text x="30" y="140" font-size="16" fill="#b57f00">Equilateral</text> <!-- Isosceles --> <polygon points="210,130 270,130 240,70" fill="#93c47d" stroke="#38761d" stroke-width="3" /> <text x="190" y="140" font-size="16" fill="#38761d">Isosceles</text> <!-- Scalene --> <polygon points="370,130 430,130 415,70" fill="#6fa8dc" stroke="#0b5394" stroke-width="3" /> <text x="350" y="140" font-size="16" fill="#0b5394">Scalene</text> </svg>
## Triangles in Real Life Look around! Triangles appear everywhere: - Roofs of houses - Bicycle frames - Traffic signs <svg width="400" height="200" viewBox="0 0 400 200" xmlns="http://www.w3.org/2000/svg"> <!-- Roof --> <polygon points="50,150 150,50 250,150" fill="#f4cccc" stroke="#cc0000" stroke-width="4" /> <!-- Bicycle frame triangle --> <polygon points="300,150 350,100 390,150" fill="#6fa8dc" stroke="#054a91" stroke-width="4" /> <!-- Traffic sign --> <polygon points="100,180 140,110 180,180" fill="#ffd966" stroke="#b57f00" stroke-width="4" /> </svg>
# Thank you for joining! Remember: Triangles are everywhere, holding our world together! <svg width="250" height="200" viewBox="0 0 250 200" xmlns="http://www.w3.org/2000/svg"> <polygon points="125,10 230,190 20,190" fill="#93c47d" stroke="#38761d" stroke-width="5" /> <text x="125" y="100" font-size="30" fill="#38761d" text-anchor="middle">Triangle</text> </svg>
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