# Pythagorean Theorem Proof Question

• May 18th 2010, 06:03 PM
Lord Darkin
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
• May 18th 2010, 06:10 PM
sa-ri-ga-ma
Quote:

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

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

You can rewrite it as

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

The factors of $c^2 - b^2 = (c+b)(c-b)$
• May 18th 2010, 06:20 PM
skeeter
Quote:

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 ...

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

cross-multiply and you're there.
• May 18th 2010, 07:12 PM
Lord Darkin
Thanks.

I got it now. (Rofl)