Proving the Pythagorean theorem

We will now prove the Pythogorian theorem: a 2 + b 2 = c 2

We can prove the theorem algebraically by showing that the area of the big square equals the area of the inner square (hypotenuse squared) plus the area of the four triangles: ( a + b ) 2 = c 2 + 4 ( 1 2 a b ) a 2 + 2 a b + b 2 = c 2 + 2 a b a 2 + b 2 = c 2

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