Draw four copies of one right triangle with legs and and hypotenuse Arrange them so they create a .
Notice that the outer square has side lengths of
Thus, it follows that the is
Alternately, the square can be seen as a composite shape, consisting of the four triangles and the inner square. Thus, its area can be expressed as the sum of the and the inner square.
The total area can be expressed as follows.
Both expressions represent the area of the larger square. Therefore, they can be set equal to each other.
The can be simplified using the fact that the is a .
Therefore, if a right triangle has legs