Given: nm ∥ xz prove: △xyz ~ △nym we know that side nm is to side xz. if we consider side ny the transversal for these parallel lines, we create angle pairs. using the , we can state that ∠yxz is congruent to ∠ynm. we know that angle xyz is congruent to angle by the reflexive property. therefore, triangle xyz is similar to triangle nym by the similarity theorem.