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
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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.
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.
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