To prove triangles MPL and MQS congruent by SAS, we need one more angle: angle P must be congruent to angle Q.
Sure, I can help you with this. The question asks for the additional information needed to prove that triangles MPL and MQS are congruent by SAS.
The SAS (Side-Angle-Side) postulate states that if two triangles have two corresponding sides congruent and the angles between those sides are congruent, then the triangles are congruent.
In the given triangles, we are given that:
* ML congruent to MS (Side)
* SQ congruent to LP (Side)
We are also given that:
* angle L congruent to angle S (Angle)
However, we are not given the congruence of the angle between sides ML and MS in triangle MPL and the angle between sides SQ and LP in triangle MQS. Therefore, we need the following additional information to prove the triangles congruent by SAS:
* angle P congruent to angle Q (Angle)
If we have this additional information, then we can conclude that triangles MPL and MQS are congruent by SAS.
So the answer to the question is: angle P congruent to angle Q.