Question

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

Explanation:

Since $\overline{NR}$ and $\overline{MQ}$ bisect each other at $S$, $S$ is the midpoint of $\overline{MQ}$. By definition of a bisector, the segments of $\overline{MQ}$ (i.e., $\overline{MS}$ and $\overline{QS}$) are congruent. With $\overline{MN} \cong \overline{QN}$, $\angle NMS \cong \angle NQS$, and $\overline{MS} \cong \overline{QS}$, $\triangle MNS \cong \triangle QNS$ by SAS.

Answer:

D. MS and QS