I love tutoring Geometry. It had been a while since I actually studied Geometry (outside of ACT and GMAT preparation). I was actually afraid that things might have changed, and I'd need to run really fast to keep up. This hasn't been the case. I pull lesson materials from a variety of resources, constantly looking for the clearest, most direct method of teaching. The book the school uses may not be the best Geometry text book -- especially with cuts in funding. Now I have a collection of Geometry books. It's fun to decide what we're going to cover in each lesson; and then search out online resources as well as the books at my disposal.
Sometimes the student has missed pieces in previous grades that are prerequisites for Geometry. It's easy to catch them up and then go on from there.
To me, the formal proofs are the most difficult topic in all of Geometry; however, they're a necessity to understanding the subject. For that reason, I first cover graphing lines; measuring angles; and finding the area, perimeter, and volume of various shapes. THEN I go back to the proofs and find the postulates and theorems that are necessary to solve the problems.
Once, this semester, my student walked in and announced he wanted to learn all about Volume! I flipped to one of the last chapters in a Geometry text, and we studied volume for the hour. It feels good to be so flexible; It's something that teachers with a class of students cannot do!