Question

which theorem shows △qmp≅△rnp?
a asa
b aas
c sas
d none of the above

Explanation:

Step1: Identify congruent parts

We can see that $\angle QPM=\angle RPN$ (vertical - angles are equal). Also, there are two pairs of non - included angles and a non - included side that seem to be congruent from the markings.

Step2: Recall triangle congruence theorems

ASA (Angle - Side - Angle) requires two angles and the included side to be congruent. SAS (Side - Angle - Side) requires two sides and the included angle to be congruent. AAS (Angle - Angle - Side) requires two angles and a non - included side to be congruent.

Step3: Determine the correct theorem

Since we have two pairs of angles and a non - included side congruent, the AAS (Angle - Angle - Side) theorem shows that $\triangle QMP\cong\triangle RNP$.

Answer:

B. AAS