See the picture attached.
We know:
NM // XZ
NY = transversal line
∠YXZ ≡ ∠YNM
1) We know that ∠XYZ is congruent to ∠NYM by the reflexive property.
The reflexive property states that any shape is congruent to itself.
∠NYM is just a different way to call ∠XYZ using different vertexes, but the sides composing the two angles are the same.
Hence, ∠XYZ ≡ ∠NYM by the reflexive property.
2) ΔXYZ is similar to ΔNYM by the AA (angle-angle) similarity theorem
The AA similarity theorem states that if two triangles have a pair of corresponding angles congruent, then the two triangles are similar.
Consider ΔXYZ and ΔNYM:
∠YXZ ≡ ∠YNM
∠XYZ ≡ ∠NYM
Hence, ΔXYZ is similar to ΔNYM by the AA similarity theorem.
