Given: NM ∥ XZ
Prove: △XYZ ~ △NYM
Triangles X Y Z and N Y M are shown. Triangle X Y Z is smaller and sits inside of triangle N Y M, sharing part of 2 sides with triangle N Y M. The hypotenuses of both triangles are parallel.
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.