1. Presented By: Alexander Sarkissian

2. Pythagoras’s Theorem  First we will start with the common right triangle.  Side a= Adjacent side  Side b= Opposite side  Side c= Hypotenuse

3.  We start out with four right triangles.  Three of these have been rotated 90 o, 180 o, and 270 o.  Each has an area of ab/2

4. Pythagoras’s Theorem Let's put them together without additional rotations so that they form a square with side c.

5. Pythagoras’s Theorem The square has a square hole with the side (a-b). Summing up its area (a-b) 2 and 2ab, the area of the four triangles is (4·ab/2).

6. Formula c 2 = (a-b) 2 +2ab = a 2 -2ab+b 2 +2ab= a 2 +b 2 Thus we simplify the equation and end up with a²+b²=c²

7. The End Sources:  http://www.cut-the- knot.org/pythagoras/index.shtml http://www.cut-the- knot.org/pythagoras/index.shtml