🧱 See It
Every right triangle has a right angle (a perfect square corner) and, opposite that corner, its longest side — called the hypotenuse. Build an actual square on each of the three sides. The areas of the two smaller squares always add up to the area of the biggest one.
✏️ Draw It
9 + 16 = 25 — every single time, for every right triangle, no matter its size.
🔢 Write It
a² + b² = c²
c is always the hypotenuse — the longest side, directly opposite the right angle. a and b are the two shorter legs.
Finding the hypotenuse: add the squares, then take the root. Finding a leg: SUBTRACT the squares instead, then take the root.
💡 Worked Examples
Example 1 — Find the hypotenuse: legs 6 and 8
- Square both legs:
6² = 36,8² = 64 - Add:
36 + 64 = 100 - Take the square root:
√100 = 10 - Answer: hypotenuse = 10
Example 2 — Find a missing leg: hypotenuse 13, one leg 5
- Square both known sides:
13² = 169,5² = 25 - Subtract (hypotenuse minus the known leg):
169 − 25 = 144 - Take the square root:
√144 = 12 - Answer: missing leg = 12
🧠 Quick Reference
a² + b² = c². Identify the right angle first, then the hypotenuse directly opposite it (always the longest side) — before touching the formula. Solving for the hypotenuse: ADD the squares. Solving for a leg: SUBTRACT the squares.