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, ∠nms 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. options: ns and qs, ms and qs, ms and rs, ns and rs

Explanation:

Step1: Identify bisected segments

Since NR and MQ bisect at S, MS=QS (MQ bisected) and NS=SR (NR bisected).

Step2: Apply SAS for congruence

△MNQ is isosceles ⇒ MN=QN; base angles ∠NMS=∠NQS; MS=QS (bisector). Thus, △MNS≅△QNS by SAS.

Answer:

MS and QS