Take a generic right triangle. Flip, rotate and scale it by multiplying each side by a factor of b. I did this by imagining that a = 1 and then b = ab. The complementary angles are marked with circles on the right.

So then construct a rotated triangle from the same input, but scaled by a factor of a, and attach it to the other one. We know that the sides marked ab are parallel, and that the angle between bc and ac is a right angle, by the properties of right, complementary and supplementary angles.

The four outside vertices form a rectangle, from the angles and also since ab = ab.

Finally, rotate and scale again, by a factor of c:

Slide them together

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