# Thread: Pythagorean Theorem Proof Question

1. ## 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

2. 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

$\displaystyle a^2 + b^2 = c^2$

You can rewrite it as

$\displaystyle a^2 = c^2 - b^2$

The factors of $\displaystyle c^2 - b^2 = (c+b)(c-b)$

3. 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 ...

$\displaystyle \frac{c+b}{a} = \frac{a}{c-b}$

cross-multiply and you're there.

4. Thanks.

I got it now.