Thread: Pythagorean Theorem Proof Question

For proof 11, why is a squared equal to (c - b)(c + b) ? I would understand the proof if I could get that one part.

Pythagorean Theorem and its many proofs

Originally Posted by Lord Darkin

For proof 11, why is a squared equal to (c - b)(c + b) ? I would understand the proof if I could get that one part.

Pythagorean Theorem and its many proofs

According to the Pythagorean theorem



You can rewrite it as



The factors of

Originally Posted by Lord Darkin

For proof 11, why is a squared equal to (c - b)(c + b) ? I would understand the proof if I could get that one part.

Pythagorean Theorem and its many proofs

looking at triangle triangle GFH , length "a" is the altitude to the hypotenuse.

using similar triangles GFH, GKF, and FKH, the following ratio between corresponding sides can be made ...



cross-multiply and you're there.

Thanks.

I got it now.