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.

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Аноним Аноним · Answer 1 · 2019-02-04T06:19:56+01:00

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]

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MrRoyal MrRoyal · Answer 2 · 2021-10-25T18:11:47+02:00

Two triangles are similar, if they have similar corresponding sides and angles.

Triangle XYZ is similar to triangle NYM by the AAS similarity theorem.

From the question, we have:

Because, NY is a transversal.

It means that: angles YNM and YXZ are alternate angles of a transversal.

So, we have:

[tex]\mathbf{\angle YNM \cong YXZ}[/tex] ----Alternate angle

Both triangles share the same vertex at point Y.

So, we have:

[tex]\mathbf{\angle NYM \cong XYZ}[/tex] --- Common vertex at Y

Going by the above highlights, we have:

Hence, triangle XYZ is similar to triangle NYM by the AAS similarity theorem.

Read more about similar triangles at:

https://brainly.com/question/14926756