My high school class had hand drawn first semester, autoCAD second semester. (I happened to only be taking the second semester, because I needed another class to fill that semester, so I personally only experienced the autoCAD component)
From my comments you can see that it is in my experience, and my school was not top-rated at all. It was wrong of me to assume everyone else had the same experience.
I'm not even sure I know what a geometric proof is, so I'd say no?
Our teacher would just ask us to solve this sort of exercises with a compass and a ruler, and then he'd grade the tests by checking whether the process to reach the solution made sense (i.e.: I'm pretty sure that level 20 was one of the questions in my midterms). He would have explained the resolutions for most of them in previous lectures, but others were new to us. I can't remember if an additional written proof was required.
I think that fits the requirements for a "fun game".
Also wouldn't a CAD program have bisect and what this calls compass2 from the get go?