You know the Pythagorean Theorem as a theorem regarding areas, in particular, the sum of the areas of the squares constructed on the legs of a right triangle is equal to the area of the square built on the hypotenuse. You also know from http://www.geogebratube.org/student/m127692 that the Pythagorean Theorem holds for any regular polygons constructed on the sides of a right triangle. Did you know the Pythagorean Theorem holds for any similar figures constructed on the sides of a right triangle?
Drag the GREEN point to change the shape of the polygons.
Drag the RED points to change the size of the right triangle.