Consider this figure of one square inscribed in another:

Write this equation for the area of the larger square:

(a+b)^{2}=c^{2}+ 4(ab/2)

Condensing and expanding we have:

a^{2}+ 2ab+b^{2}=c^{2}+ 2ab

Which reduces to:

c^{2}=a^{2}+b^{2}

QED.

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