Question

given \\( \overline { r t } \parallel \overline { s p }, \overline { r q } \cong \overline { q p }, \overline { r p } \\) bisects \\( \overline { s t } \\) at \\( q \\). prove \\( \triangle r q t \cong \triangle p q s \\). tamin is working to prove the triangles congruent using sas. after stating the given information, he states that \\( \overline { t q } \cong \overline { q s } \\) by the definition of segment bisector. now he wants to state that \\( \angle r q t \cong \angle p q s \\). which reason should he use? alternate interior angles theorem corresponding angles theorem linear pair postulate vertical angles theorem

Explanation:

Vertical angles are formed when two lines intersect. In this case, \(\angle RQT\) and \(\angle PQS\) are vertical angles. By the vertical angles theorem, vertical angles are congruent. So, the reason Tamin should use is the vertical angles theorem.

Answer:

vertical angles theorem