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Pythagorean theorem[pə‚thag·ə′rē·ən ′thir·əm]
a theorem in geometry stating the relationship between the sides of a right triangle. The theorem was evidently known before the time of Pythagoras (sixth century B.C.), but its general proof is ascribed to him. Originally, the theorem stated the relationship between the areas of squares constructed on the hypotenuse and legs of a right triangle: the square on the hypotenuse is equal in area to the sum of the squares on the legs. The customary, more concise, formulation of the Pythagorean theorem is that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the legs. The converse of the Pythagorean theorem is also true: if the square of one side of a triangle is equal to the sum of the squares of the two other sides, the triangle is a right triangle.