Proof of the Pythagorean theorem using scaling and lengths.

Proof of the Pythagorean theorem using scaling and lengths, not areas. Three copies of a right triangle of sides a, b, c. The pink one is actually a times bigger, the blue, b times bigger and the green c times bigger than the original green one. These three triangles can form a rectangle. The opposite sides are congruent and measure c² and a²+b².
Prove that the three triangular pieces of this puzzle do fit perfectly to form a rectangle.