How do you compare euclidean elliptic geometry and non-euclidean geometry?

In Euclidean geometry parallel lines are always the same distance apart. In non-Euclidean geometry parallel lines are not what we think of a parallel. They curve away from or toward each other. Said...

Geometry that is not on a plane, like spherical geometry

The two commonly mentioned non-Euclidean geometries are hyperbolic geometry and ellptic geometry. If one takes "non-Euclidean geometry" to mean a geometry satisfying all of Euclid's postulates...

true

This is geometry that is based on ordinary space-- space as we normally consider it. This is the ordinary space of 3 dimensions as you can imagine them in the coordinate system. Planes are flat, and...