Pythagorean Theorem Proof
Pull up a chair, and don’t make a move!
We’ve got something we really must prove
‘Bout sides of a right triangle, num’bring three.
You’ve somewhere to be? I won’t hear your plea!
A plus B, squared, as in the picture I drew, (A+B)^2= C^2 + 4AB/2
equals C squared plus 4 times AB over two.
Next, smartly observe that four, two divides, (A+B)^2= C^2 + 2AB
and promptly subtract 2AB from both sides. (A+B)^2–2AB= C^2+2AB-2AB
Expand A plus B, squared; and then simplify. A^2+B^2 +2AB–2AB= C^2
You’ve just used your math to well justify A^2 + B^2 = C^2
and prove what Pythagoras wisely declared -
A squared plus B squared is exactly C squared.
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