Question

given: rt || sp, rq ≅ qp, rp bisects st at q. prove: △rqt ≅ △pqs. tamir is working to prove the triangles congruent using sas. after stating the given information, he states that tq ≅ qs by the definition of segment bisector. now he wants to state that ∠rqt ≅ ∠pqs. which reason should he use? linear pair postulate, alternate interior angles theorem, corresponding angles theorem, vertical angles theorem

Explanation:

Step1: Identify angle relationship

∠RQT and ∠PQS are opposite at intersection Q of RP and ST.

Step2: Apply angle theorem

Opposite angles (vertical angles) are congruent by vertical angles theorem.

Answer:

vertical angles theorem