Great feedback!

I can solve the "point moving too fast" thing.

For each shape I wanted it to be able to rotate. Most textbooks etc show the quadrilateral "unrotated" (example: the trapezoid always has its parallel sides horizontal). So I wanted to be able to show it in different "poses". I may not have selected the right way to move things, though. Can you give specific cases that are counter-intuitive? Maybe I can think of another way.

Also, if you select another shape, the points return to within the drawing area.

US: Trapezoid / UK: Trapezium is a big problem, which is just gonna stay that way till education authorities wake up. I put a note on it.

BTW: should it be called "Animation" or "Interactive"?

I vote for interactive. Animated suggests you just sit there and watch them move.

I found an example of the counter-intuivity. Let's say you have a rectangle ABCD with A in the top-left corner and B in the top-right. If I drag point A horizontally, then the rectangle stretches horizontally. But if I drag it vertically, then the rectangle rotates, which is confusing. And the same goes for all the other points. It might be better to make A and C always change the scale of it and B and D always rotate, although I'm not certain. There are lots of other similar situations to that. It's only a minor quibble though, it's still easy enough to use.

Another fault I found is that if I turn the diagonals on then it highlights line AD as well as the 2 actual diagonals. Also, it won't let me make a kite that has a reflex angle, even though they're perfectly fine quadrilaterals.

I was also going to suggest that you showed that squares were rectangles, like you showed that various things were parallelograms, but then I realised that squares were also rhombuses (rhombi?) and so you'd also have to show that somehow and that would just complicate things.