Pythagorean Theorem
📋 What it is
In a right triangle, the square on the longest side equals the sum of the squares on the other two: a² + b² = c².
🗣️ Coach says
The Pythagorean theorem is a superpower: if a triangle has a right angle, the two short sides "squared and added" always equal the long side "squared". It lets you find a distance you can't measure directly.
🧠 Memory hook
a² + b² = c². The c is ALWAYS the longest side (the hypotenuse), across from the right angle.
😂 Giggle
Why should you never argue with a 90-degree angle?
Because it's always right!
😲 Whoa!
The 3-4-5 triangle was used by ancient Egyptians with a knotted rope to make perfect right angles for building — no protractor needed.
✅ Quick check: A right triangle has legs 3 and 4. How long is the hypotenuse?
Say your answer out loud first — then reveal.
5, because 3² + 4² = 9 + 16 = 25, and √25 = 5.
a² + b² = c² gives c² = 25, so c = 5.
🧪 Try it! (2 minutes)
Cut a right triangle from paper with legs 3 cm and 4 cm; measure the long side — it's ~5 cm.