Question

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.

Answer 1

Answer:

We know that side NM is PARALLEL to side XZ. If we consider side NY the transversal for these parallel lines, we create angle pairs. Using the CORRESPONDING ANGLES THEOREM, we can state that ∠YXZ is congruent to ∠YNM. We know that angle XYZ is congruent to angle NYM by the reflexive property. Therefore, triangle XYZ is similar to triangle NYM by the AA similarity theorem.

Step-by-step explanation:

answers on e2020

Answer 2

Solution:

In  ΔXYZ and ΔNYM

NM ║XZ, YNX is a transversal.

1. ∠YNM= ∠ YXZ→→→[Alternate angles, ∵ NM║XZ, and YNX is a transversal]

2. ∠NYM=∠XYZ [ ∠Y is common between two triangles,that is by reflexive property]

→→ΔXYZ ~ ΔNYM ⇒{Angle-Angle Similarity]