NON EUCLIDEAN GEOMETRY

Prove the following variant of Angle -Side - Side

Claim: Consider Triangles ABC and triangle A'B'C' on Euclidean and Hyperbolic plane such that angle BAC is congruent to angle B'A'C', AB is congruent to A'B' and BC is congruent to B'C'.

Then either Triangle ABC is congruent to Triangle A'B'C', or measure of angle BCA + measure of angle B'C'A' is equal to 180 degrees