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Subject: "Proof #25 of the Pythagorean Theorem"

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Conferences The CTK Exchange Middle school Topic #138
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Catherine

guest

Mar-06-10, 05:11 PM (EST)

"Proof #25 of the Pythagorean Theorem"

I don't really get why a☐LMOA=a☐LKCA=a☐ACDE and a☐HMOB=a☐HKCB=a☐HKDF.
Please explain why that is true.

Thanks,
Catherine

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alexb
Charter Member
2477 posts

Mar-06-10, 05:17 PM (EST)

1. "RE: Proof #25 of the Pythagorean Theorem"
In response to message #0

It's all about shearing:

Parallelograms LMOA and LKCA have a common base AL and and collinear opposite sides OM and CK. Hence they have the same areas.

Parallelograms LKCA and ACDE have a common base AC and collinear opposite sides LK and DE.

Parallelograms HMOB and HKCB have a common base BH, etc...

Parallelograms HKCB and HKDF have a common base HK, etc...

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