Every year I subject myself to a lesson along these lines, every year I get the same result, and every year I keep coming back for more. Didn't Einstein have something to say about that?
Anyway, I finally decided to bust out the compasses, but only for my honors classes. I really think the compass is an amazing piece of technology and truly underscores the idea of congruence without equivalence, but those ideas are incredibly abstract and very difficult for my students to grasp, so the lesson almost never lands the way I hope it would.
I started by showing the different varieties of compass and emphasizing that they all do the same thing; create a set of points that are all equidistant from a common point. Using just a compass and a straightedge, the Greeks were able to discover most of classical geometry in the absence of a decimal numbering system. Pretty awesome, right? Well, not to 15 year olds anyway.
I demo the basic construction of copying a line segment using a document camera. At this point, I haven't given out the compasses, because all heck will break loose when I do (I've learned at least that much in my years trying to do this). I have a pre-printed packet of 4 basic constructions that I hand out along with the compasses, and then we walk through creating a parallel line through a point while showing a flash animation on the screen.
No joke, it actually worked a little this year. No idea why, but the results were more along the lines of what I hope for. What was lacking was the appreciation aspect of it. Kids don't really care about why a compass is useful or what we can do with it. Nobody wanted to explore the rest of the constructions at the end of the period or see what else they could do.
I hope I can devote another class period to at least the angle bisector construction, but it's hard to justify spending so much time on a skill that isn't really going to enhance their understanding of the content.