Question

Which relationship in the diagram is true?
ΔMNR ≅ ΔMNS by ASA
ΔRMS ≅ ΔRQS by AAS
ΔSNQ ≅ ΔSNM by SSS
ΔQNR ≅ ΔMNR by HL

Answer 1

Answer:

ΔRMS ≅ ΔRQS by AAS

Step-by-step explanation:

Answer 2

Given :  

∠RMS ≅ ∠RQS

RS bisects ∠MRQ

To Find : Which relationship in the diagram is true?

ΔMNR ≅ ΔMNS by ASA

ΔRMS ≅ ΔRQS by AAS

ΔSNQ ≅ ΔSNM by SSS

ΔQNR ≅ ΔMNR by HL

Solution:

∠RMS ≅ ∠RQS

RS bisects ∠MRQ

=> ∠SRM ≅ ∠SRQ

RS ≅  RS    ( reflexive property )

=> ΔRMS ≅ ΔRQS by AAS

AAS  - Angle angle Side

AAS  - Angle angle Side  Congruence:

If two angles and a nonincluded side of the first triangle are congruent to two angles and the corresponding nonincluded side of the second triangle, then those triangles are congruent.

Hence correct answer is :

ΔRMS ≅ ΔRQS by AAS

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