The square of (c+h) = the square of c+the square of h+2 * c * h.

The square of (a+b) = the square of a+the square of b+2 * a * b.

The two right angles of a right triangle are A and B, the hypotenuse is C, and the height on the hypotenuse is H.

So the square of a+the square of b = the square of c; a*b=h*c

So the square of (a+b) = the square of a+the square of b+2 * a * b = the square of c+2h * c.

therefore

The square of (a+b)+the square of H = the square of C+H.

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