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.

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