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The Pythagorean Theorem

The Pythagorean Theorem is named after Pythagoras of Samos , a mathematician who was also a religious leader, and believed that all things in the universe were composed of numbers.

He is supposed to have been the first to have proved this theorem about right triangles:

Pythagorean Theorem. In a right triangle with legs of lengths a and b and hypotenuse of length c , the following equation is true:

c 2 = a 2 + b 2

(There are many different ways to prove this.)

The hypotenuse of a right triangle is the side opposite the right angle.

Below is a graphical representation. The theorem states that the sum of the areas of the blue and red squares is equal to the area of the green square.

Important : Remember that the Pythagorean Theorem is true only for right triangles – triangles which have a 90 ° angle.

The converse of the theorem is also true: if a triangle has sides of lengths a , b , and c , and c 2 = a 2 + b 2 , then it must be a right triangle .

See also Pythagorean Triples .