Side-Angle-Side Similarity Theorem. If the lengths of two sides of one triangle are proportional to the lengths of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar.
We are asked to determine whether the given triangles are similar.
Notice that there is a pair of vertical angles. These angles have equal measures. Therefore, ∠ MNR = ∠ PNQ.
As we can see, two angles of one triangle are congruent to two angles of another triangle. Therefore, by the Angle Angle Similarity Postulate the triangles are similar.
△ NRM ~ △ NPQ
