Euclid's proof of Pythagoras' theorem

This is an illustration of the classical proof of [b]Pythagoras' theorem[/b]. There are many other proofs, but this is the one from [b]Euclid[/b].

Play around with the vertices, A, B & C. Can you describe carefully the construction shown here? Why are the four coloured triangles equal in area (green=yellow=pink=blue)? Can you find a rectangle having the same area as the square BCIH? How can you conclude that [math]|AB|^2 = |AC|^2+|BC|^2[/math]?