Question

given rt || sp, rq = qp, rp bisects st at q
prove: △rqt ≅ △pqs
tanner 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?
corresponding angles
alternate interior angles
theorem
theorem
linear pair postulate
vertical angles theorem

Explanation:

Step1: Analyze the given information

We have \(RT\parallel SP\), \(RQ = QP\), and \(RP\) bisects \(ST\) at \(Q\) (so \(TQ=QS\)). We need to find the reason for \(\angle RQT=\angle PQS\).

Step2: Recall the vertical angles theorem

Vertical angles are the angles opposite each other when two lines cross. In the figure, \(\angle RQT\) and \(\angle PQS\) are formed by the intersection of lines \(RP\) and \(ST\). According to the vertical angles theorem, \(\angle RQT\) and \(\angle PQS\) are congruent.

Answer:

vertical angles theorem