I need to show that every isometry in the plane is a composition of at most three reflections. Now every isometry in the plane is one of the four: 1.translation. 2.rotation. 3.reflection. 4.glide. now obviously refelction is itself. now for translation i showed with a picture that we need only two reflections. for rotation we need something like 3 reflections, and also for glide, which answers another question is it possible for glide to be a composition of just two reflection, i don't think so, but don't see how to show this. Is any of what i wrote make sense? thanks in advance.