The animation system can be used to illustrate geometric constructions. This is not a new idea, but it falls directly out of the way the system is set up: given some geometric algorithm, give it some geometric data as input, and it will give you geometric data as output.
To illustrate a geometric construction, we need to make a minor change to the way the event history is handled: Instead of saving the event history and allowing the user to play it, we apply geometric events immediately. For example, if an algorithm says "add a triangle", we do not postpone adding the triangle until later.
Using this trick, I have prepared a demonstration of three theorems on triangles: