If I had just read the proofs on my own I'm sure this wouldn't have happened but for this class we (the students) have to take turns teaching proofs to the rest of our classmates. Our mentor is there to catch us when we fall and straighten us out when we tangle ourselves up (this is key!) but we do most of the work on our own. And that is how you really learn something inside and out. The first couple proofs aren't so difficult but as they get more complicated they get very tricky to follow.
I was inspired by one of my classmates who made cool color-coded diagrams for all the proofs she taught (using Corel Draw - I want that program!) and I started to do likewise (in Powerpoint, sufficient but inferior). Making these diagrams is what I find really fun and the process really, really helps me learn the proof inside out. Even better, when you make a good, clear diagram it's really easy to follow Euclid's logic and the stuff he proves is clever/cool. Without a color coded, easily labelled diagram you spend all your mental energy trying to follow which two angles, triangles or parallelograms Euclid is talking about and I can never keep it all straight in my head long enough to follow the logical argument the proof is making. But when all you have to remember is the blue triangle and the pink triangle, it's easy. Here is an example.
Check out this proof with a rendering of Euclid's diagram
Then look at the version I created. Do you get it? Can you follow it? So much fun! If anyone wants to study Euclid Book I, I'd LOVE to help you. I think it's cool that Abraham Lincoln credited Euclid with teaching him logic and his grasp of logic was hugely instrumental in helping him win the Lincoln/Douglas debates.