Proof of Pythagorean Theorem Using Similar Triangles
1)All 3 triangles are right triangles.
2)Label the sides of all 3 triangles a, b, and c, with c being the hypotenuse.
3)Multiply all sides of the smallest triangle by a, all sides of the medium triangle by b, and all sides of the biggest triangle by c.
4)The triangles are now similar triangles, since they have the same 3 sides (a, b, c) all multiplied by a constant.
5)Try to arrange the two smaller triangles so that they fit inside the larger triangle. If you arrange them properly, the side that they share should touch, and the sides that they share with the big triangle should correspond.
6)Compare the hypotenuse of the big triangle when it’s filled with the little triangles and when it’s empty to come up with the Pythagorean Theorem: