Question

1. alejandra completed a two - column proof as shown. given: mp || tw and ht || kv prove: ∠tvz≅∠hnr alejandra says this is the only way to prove ∠tvz≅∠hnr. explain whether you agree with her.

Explanation:

Step1: Identify given parallel - lines

We are given $MP\parallel TW$ and $HT\parallel KV$.

Step2: Use angle - congruence rules for parallel lines

For $MP\parallel TW$, $\angle TVZ\cong\angle KPR$ as alternate exterior angles. For $HT\parallel KV$, $\angle HNR\cong\angle KPR$ as corresponding angles.

Step3: Apply transitive property

Since $\angle TVZ\cong\angle KPR$ and $\angle HNR\cong\angle KPR$, by the transitive property of congruence, $\angle TVZ\cong\angle HNR$.

Step4: Analyze uniqueness of proof

No, this is not the only way. We could also use other angle - relationships such as vertical angles and different combinations of parallel - line angle rules. For example, we could find other sets of congruent angles related to $\angle TVZ$ and $\angle HNR$ through a different sequence of parallel - line and transversal relationships.

Answer:

No, this is not the only way to prove $\angle TVZ\cong\angle HNR$.