# Pythagorean Theorem Proof Question

#### sa-ri-ga-ma

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

Lord Darkin

#### skeeter

MHF Helper
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.

Lord Darkin

#### Lord Darkin

Thanks.

I got it now. (Rofl)