This hits close to me as a possible reason why I could never get good at solving geometry problems, solid geometry especially. Most problems would be trivial when one assumes specific preconditions, but my mind was always wandering around, looking at all potential sides of a problem and I could never solve anything. To quote the author from my particular pov:
a problem has multiple potential causes, and you have every reason to believe in one of them, even though another is secretly responsible.
Reminds me that I need to pick up a book and re-learn the damn thing. It really saddens me that I suck at geometry.
I think you should try looking at geometry more like a creation initially then a problem. In this manner you can see assumptions as just building up more simple worlds with those constraints. I have found this view helps when teaching geometry as it empowers the mind.
