A Square Proof

Strategies and Hints

  1. Any of the four right triangles in the figure can be used for the sides a, b, and c.

  1. The length of the side of the inner square appears in the proof as the difference of the legs of the triangles.

  2. With a "hole" of zero area, the first equation is:

Solution

Continuing from the expression in part 2, the complete proof is:

 

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