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

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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.

Mathematics

1 answer:

lawyer [12.5K] · Answer 1 · 2026-03-01T17:48:25+03:00

Answer:

Parallel

corresponding angles theorem

NYM

AA

Step-by-step explanation: I DID IT ON EDGE!: )

We know that side NM is _________________

✔ parallel

to side XZ. If we consider side NY as the transversal, angle pairs are formed. According to the _____________

✔ corresponding angles theorem

, it follows that ∠YXZ is congruent to ∠YNM. Also, angle XYZ is congruent to angle _____________

✔ NYM

due to the reflexive property. Hence, triangle XYZ is similar to triangle NYM by the _____________

✔ AA

similarity theorem.