Homeschool World Forum

If you're basing your proof off x and y, you're going to have to be able to name x and y. Given, if you're just studying for a test, some tests may list theorems and definitions at the start so you don't have to memorize everything, but if all you care about is the test, then why take geometry in the first place? Geometry proofs are more of an classical art form than a required topic, something you either do for fun (or well-roundedness), or skip entirely.

On a personal level, I went up through Calculus III and did quite well, but I never did focus much on geometry per se. If I had been forced to, however, I would have memorized everything just in case.

Maybe someone more helpful can weigh in here

I have Painless Geometry, by Lynette Long, and hope to do it with my children soon. It helps them get a good start in geometry, so they can understand it and not just memorize things. I think this book would help your children be able to figure out how to do use the theorems that would help them on tests. Yes, teach them how to do proofs. They won't know if they are good at it unless they get a chance to do it.
I studied geometry and think it teaches you how to think and helps you understand algebra, and it's easier than algebra, so do it first
Also, check out Harold Jacobs' textbooks. He is a great author and I know he has one for geometry. I found them at the library(bigger suburban library near Chicago, not my small local library).

They should know the important ones, anyway. If you have a copy of Euclid's Elements, they should memorize the axioms and postulates and important definitions.

When I learned it, I had a sheet of paper with the first 48 propositions from the book on it which I reference during tests, but I had to memorize the definitions, axioms and postulates. It seems to be an effective way to learn.