Question

mark any congruent parts on the triangles that can be proved. what additional piece of information is required to prove the triangles congruent by aas ≅?

Explanation:

Step1: Identify congruent parts

From the diagram, we can see that \( UT = UT \) (common side), and there are two pairs of congruent angles (marked in the diagram).

Step2: Recall AAS congruence criterion

The AAS (Angle - Angle - Side) congruence criterion states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.
We already have two pairs of congruent angles. So, we need a pair of non - included sides to be congruent. That is, we need \( \angle D\) and \( \angle S\) to be congruent (or \( \angle DUT\) and \( \angle SUT\) are already marked as congruent, \( UT\) is common, so we need \( \angle DTU\cong\angle STU\))

Answer:

We need \( \angle DTU\cong\angle STU\) (or a corresponding non - included angle pair) to prove \( \triangle DUT\cong\triangle SUT\) by \( AAS\).