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: $\begin{array}{rcl}{(a+b)}^{2}& =& {c}^{2}+4\cdot \left(\frac{1}{2}ab\right)\\ {a}^{2}+2ab+{b}^{2}& =& {c}^{2}+2ab\\ {a}^{2}+{b}^{2}& =& {c}^{2}\end{array}$

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