Here is a right triangle, split along the altitude to the hypotenuse.

This creates three similar triangles: ABD, CAD, and CBA. Using similarity, you can show

$${a}^{2}=cx$$

and also

$${b}^{2}={c}^{2}-cx$$

which is all you need to show that

$${a}^{2}+{b}^{2}={c}^{2}$$

The neat part is that it requires no argument about areas at all.

## No comments:

## Post a Comment