My favourite proof of Pythagoras’ Theorem is this one, for the simple fact that the maths required to understand it is as basic as possible, and the constructions requires only two cuts. With this worksheet students can see that, no matter the dimensions, the theorem stays true.

It is also quite easy for students to create their own versions (using grid paper). Students should cut along the solid lines only. The area of the two squares are a²+b², but if they rearrange the pieces they will form a large square of area c².

I also have a simple GeoGebra demonstration of Pythagoras’ Theorem here.