The Theorem of Pythagoras by shear mapping

In this Worksheet you can explore the connection between the legs of a right triangle and its hypotenuse. You can move points A, B and C in a way that the triangle stays right angled.
To proof the theorem you can move the big red and blue points along given lines. Can you come up with an explanation why this proofs the theorem? (Hint: What do all paralellogramms with given height and given length of the parallel sides have in common?)