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?

At Q, the lines intersect, so ∠RQT and ∠PQS are opposite, or vertical, angles. Vertical angles are congruent, so Tamir should use the vertical angles theorem. The alternate interior and corresponding angles theorems require parallel lines, which are not given.

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