Question

given: $overline{rt}paralleloverline{sp}$, $overline{rq}congoverline{qp}$, $overline{rp}$ bisects $overline{st}$ at q. prove: $\triangle rqtcong\triangle pqs$. tamir is working to prove the triangles congruent using sas. after stating the given information, he states that $overline{tq}congoverline{qs}$ by the definition of segment bisector. now he wants to state that $angle rqtcongangle pqs$. which reason should he use? alternate interior angles theorem corresponding angles theorem linear pair postulate vertical angles theorem

Explanation:

∠RQT and ∠PQS are vertical - angles. Vertical angles are formed by two intersecting lines and are always congruent. The vertical angles theorem states that vertical angles are congruent.

Answer:

vertical angles theorem