A NEW PROOF OF PYTHAGOREAN THEOREM

In this short paper, we introduce a new geometric proof of the Pythagorean Theorem (PT). The PT states that the sum of squares of short legs of a right triangle is equal to the square of the hypotenuse [1]. In reference to Figure 1, the area A of the parallelogram RUHI is given by: 2 2 Base Height ( )( ) 2 A a b a b a b ab = × = + + = + + (1) The same area can also be expressed as the sum of the areas of the four of right triangles 1, 2, 3 and 4 and the two isosceles right triangles 5 and 6: 2 2 4( / 2) 2( / 2) 2 ab c c ab + = + (2) Equating (1) and (2) we find that 2 2 2 c a b = + which completes the proof.