PROOF OF PYTHAGORAS THEOREM USING VEDIC MATHEMATICS

Let's start by looking at a square whose side length is (a+b). We can mark a point on the side that divides it into segments of length a and b. Here are three examples, using different lengths for legs a and b:

Inside the blue square let's construct a yellow square of side length c. Its corners must touch the sides of the blue square. The remainder of the space will consist of four blue congruent abc triangles. Here it is for our example squares:

In each case, the area of the larger blue square is equal to the sum of the areas of the blue triangles and the area of the yellow square.

Since the area of a square is (side length)2 and the area of a triangle is 1/2(base)(height), we can write the equation:

(a+ b)2 = c2 + 4[(1/2)a b] (a+b)(a+b) = c2 + 2ab a2 + 2ab + b2 = c2 + 2abNow subtract the 2ab from both sides of the equation, and we have the Pythagorean theorem: a2 + b2 = c2