Question

which rule explains why these triangles are congruent? asa aas sss sas these triangles cannot be proven congruent.

Explanation:

Step1: Analyze vertical angles

$\angle QMS$ and $\angle PMN$ are vertical angles, so $\angle QMS=\angle PMN$.

Step2: Check AAS conditions

We have $\angle Q=\angle N$ (given), $SQ = NP$ (given), and $\angle QMS=\angle PMN$ (vertical angles). By the Angle - Angle - Side (AAS) congruence rule, $\triangle SQM\cong\triangle NPM$.

Answer:

AAS