In geometry, a theorem stating that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides (legs). If the hypotenuse is c units long and the lengths of the legs are a and b, then c² = a² + b².

The theorem provides a way of calculating the length of any side of a right triangle if the lengths of the other to sides are known. It is also used to determine certain trigonometrical relationships such as sin² q + cos² q = 1.

Proof!

Let a = 4 cm, b = 3 cm, and c = 5 cm

Using the Pythagorean Theorem,

c² = a² + b²

5² = 4² + 3²

25 = 16 + 9

25 = 25