What is the equivalent of "collinear" for points on a geodesic? Are they just called "cogeodesic" or something? Since the definition of a Euclidean triangle is "any three noncollinear points connected pairwise by straight line segments", I plan to define a spherical or hyperbolic triangle as "any three noncogeodesic points connected pairwise by geodesics". Does anyone have a better way of stating this?
Also, as an aside, I noticed that the area formulas for these triangles use "$\angle\alpha + \angle\beta + \angle\gamma$" or simply "$\alpha + \beta + \gamma$". Since these have a quantitative measure in radians, shouldn't they be "$m\angle\alpha + m\angle\beta + m\angle\gamma$"? If not, why not?"