Question

complete the proof that ∠prq ≅ ∠vuw.
1 qs || eg given
2 eg || tv given
3 ∠vuw ≅ ∠gfw
4 ∠gfw ≅ ∠prq
5 ∠prq ≅ ∠vuw

Explanation:

Step1: Identify corresponding - angles

Since $\overleftrightarrow{EG}\parallel\overleftrightarrow{TV}$, by the corresponding - angles postulate, $\angle VUW\cong\angle GFW$.

Step2: Identify vertical - angles

$\angle GFW$ and $\angle PRQ$ are vertical angles. By the vertical - angles theorem, $\angle GFW\cong\angle PRQ$.

Step3: Use transitive property

Since $\angle VUW\cong\angle GFW$ and $\angle GFW\cong\angle PRQ$, by the transitive property of congruence, $\angle PRQ\cong\angle VUW$.

Answer:

1. Corresponding - angles postulate; 4. Vertical - angles theorem; 5. Transitive property of congruence