The proof that δmns ≅ δqns is shown. given: δmnq is isosceles with base mq, and nr and mq bisect each other at s. prove: δmns ≅ δqns

we know that δmnq 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. therefore congruent by the definition of bisector. thus, δmns ≅ δqns by sas.

ns and ns
ns and rs
ms and rs
ms and qs

The correct option is MS and QS

Step-by-step explanation:

Given ΔMNQ is isosceles with base MQ, and NR and MQ bisect each other at S. we have to prove that ΔMNS ≅ ΔQNS.

As NR and MQ bisect each other at S

⇒ segments MS and SQ are therefore congruent by the definition of bisector i.e   MS=SQ

In ΔMNS and ΔQNS

MN=QN       (∵ MNQ is isosceles triangle)

∠NMS=∠NQS     (∵ MNQ is isosceles triangle)

MS=SQ         (Given)

By SAS rule, ΔMNS ≅ ΔQNS.

Hence, segments MS and SQ are therefore congruent by the definition of bisector.

The correct option is MS and QS