Question

given: rs bisects ∠mrq; ∠rms≅∠rqs which relationship in the diagram is true? △mnr≅△mns by asa △rms≅△rqs by aas △snq≅△snm by sss △qnr≅△mnr by hl

Explanation:

Step1: Recall angle - bisector property

Since $\overline{RS}$ bisects $\angle MRQ$, we have $\angle MRS=\angle QRS$.

Step2: Identify congruent - triangle criteria

We are given that $\angle RMS\cong\angle RQS$, and $\overline{RS}=\overline{RS}$ (common side). So, in $\triangle RMS$ and $\triangle RQS$, we have two angles and a non - included side congruent. By the Angle - Angle - Side (AAS) congruence criterion, $\triangle RMS\cong\triangle RQS$.

Answer:

$\triangle RMS\cong\triangle RQS$ by AAS