Question

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

Explanation:

Step1: Analyze vertical angles

Vertical angles are equal. So, $\angle VQU=\angle TQS$.

Step2: Analyze side - angle relationships

We know that $UQ = SQ$ (given by the tick marks). Also, if we assume that $\angle V=\angle T$ (from the figure's symmetry in terms of angle - side - angle - like structure, and the vertical angles $\angle VQU=\angle TQS$). Then we have two angles and the included side.

Answer:

ASA