Question

what additional information is needed to prove that the triangles are congruent by aas?

Explanation:

Step1: Recall AAS congruence criterion

AAS (Angle - Angle - Side) requires two angles and a non - included side to be congruent in two triangles.

Step2: Analyze given information

We have right - angles at $\angle OYZ$ and $\angle OYW$, and we know that $OY$ is common. We also seem to have one pair of angles marked as congruent (but we don't know which two triangles we are considering precisely). To use AAS, we need another pair of angles.
If we consider $\triangle OYZ$ and $\triangle OYW$, we need $\angle YOZ\cong\angle YOW$.

Answer:

$\angle YOZ\cong\angle YOW$