ASA Triangle Congruence Theorem Proof
Angle-Side-Angle (ASA) Triangle Congruence Theorem
Here you can see a proof of the ASA Triangle Congruence Theorem. Click on the checkbox for Constructions to see the construction of the figures needed in the proof. Notice that point D? can be moved along ray A'C', but the way it is constructed, it must be at a distance of AC from A'. This results in only one point. By the SAS Postulate we see that Triangle ABC is congruent to Triangle A'B'D so we have Angle ABC congruent to Angle A'B'D, but this means that C' is also on Ray B'D and thus D = C', completing the proof.
This proof is illustrated here in Euclidean Geometry. However, this same proof is also valid in Hyperbolic and Spherical Geometries as well.