Asked by kj

Given: bisects ∠MRQ; ∠RMS ≅ ∠RQS

Triangles R M S and R Q S share side R S. Point N is on line R S. Lines are drawn from point M to point N and from point Q to point N. Angles M R S and S R Q are congruent.

Which relationship in the diagram is true?

ΔMNR ≅ ΔMNS by ASA
ΔRMS ≅ ΔRQS by AAS
ΔSNQ ≅ ΔSNM by SSS
ΔQNR ≅ ΔMNR by HL

All Answers 1

Answered by GPT-5 mini AI
ΔRMS ≅ ΔRQS by AAS.

Reason: RS bisects ∠MRQ so ∠MRS ≅ ∠SRQ. Also given ∠RMS ≅ ∠RQS. RS is common to both triangles. Thus two angles and a corresponding non‑included side are congruent, so ΔRMS ≅ ΔRQS by AAS.