Pythagorean Theorem

Theorem. If $ABC$ is a right triangle, then the square of the length of the hypotenuse, the side opposite to the right angle, is equal to the sum of the squares of the other two sides.

The Law of Cosines is a generalization of Pythagorean theorem for any triangle.

Converse. If the sides of a triangle satisfy $a^2+b^2=c^2$ then the triangle is a right triangle.