Question

can you conclude that these triangles are congruent?

Explanation:

Step1: Analyze vertical angles

Vertical angles are equal. So, $\angle TSU=\angle VSW$.

Step2: Check side - angle - side (SAS) congruence

We know that $TS = VS$ (given by the tick marks), $\angle TSU=\angle VSW$ (vertical angles), and $\angle U=\angle W$ (given). But for SAS congruence, the side should be between the two angles. Here, we have two angles and a non - included side.

Step3: Recall congruence criteria

The congruence criteria are SSS (side - side - side), SAS (side - angle - side), ASA (angle - side - angle), AAS (angle - angle - side), and HL (hypotenuse - leg for right - triangles). The given information does not match any of these criteria.

Answer:

no