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If the length of the hypotenuse of each right-angled triangle is c
and the lengths of the other two sides are a and b then the diagram
on the left shows a total area of 2ab+c^{2} and the diagram
on the right shows an area of 2ab+a^{2}+b^{2}
showing that a^{2}+b^{2}=c^{2}.

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