Question

question
state what additional information is required in order to know that the triangles are congruent for the reason given.
aas
a) ∠y≅∠t or ∠z≅∠u
b) (overline{xy}congoverline{st}) or (overline{zx}congoverline{us})
c) ∠x≅∠s or ∠y≅∠t
d) (overline{yz}congoverline{tu}) or (overline{zx}congoverline{us})

Explanation:

Step1: Recall AAS congruence criterion

AAS (Angle - Angle - Side) 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.

Step2: Analyze the given triangles

We already have one angle marked in each triangle. We need one more pair of angles and a non - included side.
The non - included side must be opposite one of the congruent angles. Since we are dealing with angles and sides for AAS, we need either another pair of angles and a non - included side. Looking at the options, for AAS we need a pair of angles and a side that is not between those angles. The correct additional information would be a pair of angles and a non - included side. The side must be opposite one of the congruent angles. The correct answer is about having either $\angle Y\cong\angle T$ or $\angle Z\cong\angle U$ along with a non - included side.

Answer:

A. $\angle Y\cong\angle T$ or $\angle Z\cong\angle U$