Question

∠prs≅∠tuw. complete the proof that (overleftrightarrow{tv}paralleloverleftrightarrow{qs}).
statement\treason
1 ∠prs≅∠tuw\tgiven
2 ∠prs≅∠qru\tvertical angle theorem
3 ∠tuw≅∠qru\ttransitive property of congruence
4

Explanation:

Step1: Recall parallel - line criteria

If corresponding angles are congruent, then the lines are parallel. Since $\angle TUW$ and $\angle QRU$ are corresponding angles for lines $\overleftrightarrow{TV}$ and $\overleftrightarrow{QS}$ cut by transversal $\overleftrightarrow{WP}$.

Step2: State the conclusion for parallel lines

Based on the congruence of corresponding angles, we can conclude that $\overleftrightarrow{TV}\parallel\overleftrightarrow{QS}$.

Answer:

$\overleftrightarrow{TV}\parallel\overleftrightarrow{QS}$; Corresponding Angles Postulate