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Given: rt || sp, rq ≅ qp, rp bisects st at q prove: δrqt ≅ δpqs triangles r q t and p q s are connected at point q. lines r t and s p are parallel. the lengths of lines r q and q p are congruent. 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? alternate interior angles theorem corresponding angles theorem linear pair postulate vertical angles theorem
Vertical angles have a common vertex and are formed from opposite rays.
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Angles RQT and PQS share vertex Q, Rays QR and QP are opposite, creating line RP. Rays QT and QS are opposite, creating line ST. Hence angles RQT and PQS are vertical angles. The vertical angles theorem says those angles are congruent.
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