In Euclidean geometry, we have the following congruencies of triangles: side-side-side, side-angle-side, angle-angle-side = angle-side-angle (because of the angle sum) and side-side-angle (only if the side opposite to the angle is larger than the other given side). Angle-angle-angle does never hold.
My question is this: when are triangles congruent in the hyperbolic and the spherical case and what are the conditions under which the congruencies hold?
Does anybody know a reference where all these congruencies are derived from the respective laws of sines and cosines?