For a number of proofs see:
http://www.cut-the-knot.org/pythagoras/
Proof 6 seems to be the most straightforward.
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No it never works.
You cannot.
the standard form of the Pythagorean Theorem is :a2 + b2 = c2
The Pythagorean theorem is a2 + b2 = c2
The Pythagorean theorem gets its name from the ancient Greek mathematician Pythagoras. He was one of the first to offer proof of the theorem.