What is wrong with the above figure?

This puzzle is telling us something important about proof.
 Could the first proof of the Pythagorean theorem be 'wrong' in the same way? Do the pieces really fit together the way they appear to do?
The first proof of the Pythagorean Theorem is OK, but it turns out that to really check that diagrammatic proof properly you need to have first proved that the angles of a triangle add to 180 degrees. That will be our next proof.