Law of Cosines

Let a, b, c be the sides of a triangle and A, B, C the angles opposite those sides. Then c² = a² + b² - 2ab cos C.

Since ab is non-zero, this proves that c² = a² + b² iff cos C = 0, which is equivalent to C being a right angle. (In other words: the Pythagorean Theorem and its converse.)