File:Pythagorean Theorem Proof.png

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A sketch of a proof to the Pythagorean Theorem drawn by me using MS-Paint.

The size of the bigger square is both ${\displaystyle \ \left(a+b\right)^{2}}$ (Because each of its sides' length is ${\displaystyle \ a+b}$) and ${\displaystyle \ c^{2}+2ab}$. (The size of the smaller square and the triangles)

Therefore -

${\displaystyle \ \left(a+b\right)^{2}=c^{2}+2ab\iff a^{2}+2ab+b^{2}=c^{2}+2ab\iff a^{2}+b^{2}=c^{2}}$

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