Question

state what additional information is required in order to know that the triangles are congruent for the reason given. aas a) $angle ycongangle t$ or $angle zcongangle u$ b) $overline{xy}congoverline{st}$ or $overline{zx}congoverline{us}$ c) $angle xcongangle s$ or $angle ycongangle t$ d) $overline{yz}congoverline{tu}$ or $overline{zx}congoverline{us}$

Explanation:

Step1: Recall AAS congruence criterion

AAS (Angle - Angle - Side) requires two pairs of congruent angles and a non - included side congruent.

Step2: Analyze given information

We know one angle is marked in each triangle. We need one more pair of angles and a non - included side.

Step3: Check options

For AAS, we need either $\angle Y\cong\angle T$ or $\angle Z\cong\angle U$ and a non - included side. Among the options, we need an angle - angle pair and a non - included side congruence. Option A gives $\angle Y\cong\angle T$ or $\angle Z\cong\angle U$ which satisfies the angle part of AAS.

Answer:

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