Thursday, 15 September 2011

What's Wrong with This Proof

Came across this proof at another blog....  I guess I would have real reservations about using this in geometry class as a "proof" of the Pythagorean Thm..   Comments?

I recently came across a proof of the Pythagorean Theorem that was new to me that gave me an aha! moment. This was given in Sanjay Gulati's excellent "Mathematics Academy" blog as a Geogebra demonstration. He does not indicate the original source of the proof. The aha! moment comes for the connection between the Pythagorean Theorem and an apparently unrelated theorem that I always teach in my elementary geometry class, the "crossed chords" theorem. The aha! moment occurs from looking at the following picture.

Then the crossed-chords theorem tells us that (c + a)(c - a) = b2, or c2 - a2 = b2.
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