From the diagram, we know that an angle and a side in one triangle are congruent with an angle and a side in the other triangle. This is not enough to claim congruence.
However, upon further investigation, we see that ∠RVS and ∠UVT are vertical angles. According to the Vertical Angles Congruence Theorem, vertical angles are congruent. Let's add this extra piece of information.
Now we have enough information to claim congruence by the ASA Congruence Theorem because we have two sets of congruent angles and a set of congruent corresponding included sides.
