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

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

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

Answer

Explanation:

Step1: Identify given information

We see one pair of equal angles ($\angle S=\angle P$) and one pair of equal sides ($SQ = PQ$). Also, $NQ$ is common to both $\triangle SNQ$ and $\triangle PNQ$.

Step2: Recall congruence rules

  • AAS (Angle - Angle - Side): Two angles and a non - included side are equal.
  • ASA (Angle - Side - Angle): Two angles and the included side are equal.
  • SSS (Side - Side - Side): All three sides are equal.
  • SAS (Side - Angle - Side): Two sides and the included angle are equal. In $\triangle SNQ$ and $\triangle PNQ$, we have $\angle S=\angle P$, $\angle SQN=\angle PQN$ (vertically opposite angles) and $NQ$ is common. So two angles and the included side are equal.

Answer:

ASA