Question

∠prq≅∠vuw. complete the proof that $overleftrightarrow{qs}paralleloverleftrightarrow{tv}$. statement reason 1 ∠prq≅∠vuw 2 ∠prq≅∠sru 3 ∠vuw≅∠sru 4 $overleftrightarrow{qs}paralleloverleftrightarrow{tv}$

Explanation:

Step1: Given information

Given $\angle PRQ\cong\angle VUW$

Step2: Vertical - angle property

$\angle PRQ$ and $\angle SRU$ are vertical angles, so $\angle PRQ\cong\angle SRU$ (Vertical angles are congruent)

Step3: Transitive property of congruence

Since $\angle PRQ\cong\angle VUW$ and $\angle PRQ\cong\angle SRU$, then $\angle VUW\cong\angle SRU$ (Transitive property of congruence)

Step4: Corresponding - angles postulate

$\angle VUW$ and $\angle SRU$ are corresponding angles. If corresponding angles are congruent, then the lines are parallel. So $\overleftrightarrow{QS}\parallel\overleftrightarrow{TV}$ (Corresponding - angles postulate)

Answer:

1. Given
2. Vertical angles are congruent
3. Transitive property of congruence
4. Corresponding - angles postulate