Question

∠sru≅∠rut. complete the proof that qs∥tv.
statement reason
1 ∠sru≅∠rut given
2 ∠prq≅∠sru vertical angle theorem
3 ∠rut≅∠prq transitive property of congruence
4

Explanation:

Step1: Recall parallel - line postulate

If alternate - interior angles are congruent, then the lines are parallel. $\angle PRQ$ and $\angle RUT$ are alternate - interior angles for lines $QS$ and $TV$ with transversal $PW$.

Step2: Complete the proof

Since $\angle RUT\cong\angle PRQ$, by the Alternate - Interior Angles Converse (if two lines are cut by a transversal so that a pair of alternate - interior angles are congruent, then the two lines are parallel), we can conclude that $QS\parallel TV$.

Answer:

$QS\parallel TV$; Alternate - Interior Angles Converse