This proof is #42 in Loomis's book. It is essentially the classical argument used to prove Pappus' generalization of Pythagoras' Theorem (p. 366 of Heath, p. 126 of Loomis). It is suggested in Howard Eves' book In Mathematical Circles (published by Prindle, Weber, and Schmidt, 1969), p. 74 and especially the pictures on p. 75 that it would make a good animation. This is the earliest reference I am aware of where the idea of an animated proof occurs.
Like many proofs, including Euclid's own, it partitions the square on the hypotenuse by dropping a perpendicular from the right angle through it. Then it performs a sequence of shears and translations to show corresponding areas are equal.
Click on the figure to start an animation, to pause it in the middle of an animation, or to reset it to its initial configuration if it is finished.
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