Pythagorean Theorem Proof Question

Jun 2009
806
275
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 \(\displaystyle c^2 - b^2 = (c+b)(c-b)\)
 
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skeeter

MHF Helper
Jun 2008
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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.
 
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