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Math Help - Pythagorean Theorem Proof Question

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    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
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    Quote Originally Posted by Lord Darkin View Post
    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)
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  3. #3
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    Quote Originally Posted by Lord Darkin View Post
    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.
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  4. #4
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    Thanks.

    I got it now.
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