Being the Brian that he is talking about, I did not ask that. However your questions are still valid. There is no universal rules that apply because there are no universal postulates that must be included a geometry. The main difference between Euclidean geometry and Hyperbolic and Elliptic Geometry is with parallel lines. In Euclidean geometry there is an axiom which states that if you take a line A and a point B not on that line you can draw one and only one line through B that does not intersect line A. In hyperbolic geometry you can draw an infinite amount of lines through point B that do not intersect line A. In elliptic geometry there is no such line though point B that does not intersect line A. Euclidean geometry is generally used on medium sized scales like for example our planet. On extremely large or small scales it get more and more inaccurate. This is all off the top of my head so please correct me if I am wrong.