Some more fun stuff

The following is for those of you who have learnt some Geometry. I wanted to show you a simple proof of Pythagoras theorem and, for that, you need to understand the following.  Feel free to ask questions if you do not understand something.

In the diagram above, PQ and XY are parallel straight lines (what does it mean?).  

And, AB=BE (that means, if you slide the green parallelogram along the parallel lines as below, you will see that the base of the green parallelogram coincides with the base AB of the rectangle).

FACT:  If you have such a set up as the green parallelogram and the red rectangle as seen here, then the area of the rectangle is same as the area of the parallelogram.