Question

the proof that △mns ≅ △qns is shown. select the answer that best completes the proof. given: △mnq is isosceles with base (overline{mq}), and (overline{nr}) and (overline{mq}) bisect each other at s. prove: △mns ≅ △qns we know that △mnq is isosceles with base (overline{mq}). so, (overline{mn} cong overline{qn}) by the definition of isosceles triangle. the base angles of the isosceles triangle, ∠mns and ∠qns, are congruent by the isosceles triangle theorem. it is also given that (overline{nr}) and (overline{mq}) bisect each other at s. segments ______ are therefore congruent by the definition of bisector. thus, △mns ≅ △qns by sas. options: ns and qs; ns and rs; ms and rs; ms and qs

Explanation:

When two line segments bisect each other, the segments created at the intersection point are congruent. Here, $\overline{NR}$ and $\overline{MQ}$ bisect each other at $S$, so the segments from the intersection are $\overline{MS}$ and $\overline{QS}$, which are congruent. This pair, along with the already established congruent sides and angles, satisfies the SAS congruence criterion for the triangles.

Answer:

MS and QS