## Tuesday, December 10, 2013

### Proving the Pythagorean theorem with similarity

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.