L Lord Darkin Oct 2009 128 5 May 18, 2010 #1 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

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

S sa-ri-ga-ma Jun 2009 806 275 May 18, 2010 #2 Lord Darkin said: 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 Click to expand... 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 \(\displaystyle c^2 - b^2 = (c+b)(c-b)\) Reactions: Lord Darkin

Lord Darkin said: 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 Click to expand... 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 \(\displaystyle c^2 - b^2 = (c+b)(c-b)\)

skeeter MHF Helper Jun 2008 16,216 6,764 North Texas May 18, 2010 #3 Lord Darkin said: 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 Click to expand... 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. Reactions: Lord Darkin

Lord Darkin said: 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 Click to expand... 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.