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.

Since NM is parallel to XZ and NY is a transversal, ∠YXZ and ∠YNM are congruent by the alternate interior angles theorem. The triangles also share the angle at Y, so ∠XYZ is congruent to ∠NYM by the reflexive property. With two pairs of congruent angles, the triangles are similar by AA; the matching choice is C) AA.

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