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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