Bleaug states:
Let's take a, b, c to be the sides of A, B, C squares
By construction, the sum of the two shorter sides of D is equal to c. Same result for E.
All right triangles in the picture are similar, so are D and E.
Similar triangles with equal lengths implies D and E are identical (assertion 2)
The two shorter sides of D and E are a and b. So a+b=c (assertion 1)
Triangle D is to F as G is to E, as b is to a. So F/D=E/G=(b/a)^2. Since E=D we get F.G=E^2=D^2 (assertion 3)
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