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Pythagorean Theorem Poof

Pythagorean Theorem

A visual geometric proof — adjust the triangle to explore

a² + b² = c²
a = 3 b = 4 c = 5.00
9 + 16 = 25  ✓

Adjust Triangle

a3
b4

Proof Steps

1
Draw a right triangle with legs a, b and hypotenuse c.
2
Construct a square on each side. Their areas are a², b², and c².
3
The two smaller squares can be rearranged to exactly fill the large square — no gaps, no overlaps.
4
Therefore a² + b² = c² holds for every right triangle. ∎
How it works: The proof constructs a square on each side of the right triangle. The red square has area a², the blue square b², and the green square on the hypotenuse c². Since the two smaller squares can always be rearranged to perfectly fill the larger one, a² + b² = c² must be true for every right triangle. Use the sliders to try any legs you like and watch the equality hold! ✓