given: $overline{rs}$ bisects $angle mrq$; $angle rmscongangle rqs$. which relationship in the diagram is…

given: $overline{rs}$ bisects $angle mrq$; $angle rmscongangle rqs$. which relationship in the diagram is true? $\triangle mnrcong\triangle mns$ by asa $\triangle rmscong\triangle rqs$ by aas $\triangle snqcong\triangle snm$ by sss $\triangle qnrcong\triangle mnr$ by hl

given: $overline{rs}$ bisects $angle mrq$; $angle rmscongangle rqs$. which relationship in the diagram is true? $\triangle mnrcong\triangle mns$ by asa $\triangle rmscong\triangle rqs$ by aas $\triangle snqcong\triangle snm$ by sss $\triangle qnrcong\triangle mnr$ by hl

Answer

Explanation:

Step1: Recall triangle - congruence postulates

ASA (Angle - Side - Angle): Two angles and the included side of one triangle are congruent to two angles and the included side of another triangle. AAS (Angle - Angle - Side): Two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle. SSS (Side - Side - Side): All three sides of one triangle are congruent to all three sides of another triangle. HL (Hypotenuse - Leg): For right - triangles, the hypotenuse and one leg of one right - triangle are congruent to the hypotenuse and one leg of another right - triangle.

Step2: Analyze the given information

We know that $\overline{RS}$ bisects $\angle MRQ$, so $\angle MRS=\angle QRS$. Also, $\angle RMS = \angle RQS$ and $\overline{RS}=\overline{RS}$ (common side).

Step3: Determine the congruent triangles

In $\triangle RMS$ and $\triangle RQS$, we have two angles ($\angle RMS=\angle RQS$ and $\angle MRS = \angle QRS$) and a non - included side ($\overline{RS}$). By the AAS (Angle - Angle - Side) congruence postulate, $\triangle RMS\cong\triangle RQS$.

Answer:

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