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Pythagorean Theorem:  A theorem that states that in a right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs.
 This theorem is one of the most famous and useful theorems in geometry. Pythagoras (580-496 B.C.), a Greek mathematician, was the first to prove this theorem, so it has become known as the Pythagorean Theorem. However, it appears that the Babylonians may have been aware of the theorem because they were using its converse (If the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs, then the triangle is a right triangle) more than 1300 years before Pythagoras. It is a theorem that states a relationship that exists in any right triangle. If the lengths of the legs in the right triangle are a and b and the length of the hypotenuse is c, we can write the theorem as the following equation:   A model of the theorem is shown below. Squares have been constructed on the sides of the right triangle and the area of each square has been dissected into squares. Count the gridded cells in the two squares constructed on the legs of the triangle. They should add up to the number of gridded cells in the square constructed on the hypotenuse. Many people have come up with their own version of the proof of the Pythagorean Theorem. Even President Garfield wrote a special version of the proof in 1876. Click to see Garfield's proof of the Pythagorean Theorem.