Question

state what additional information is required in order to know that the triangles are congruent by asa. asa a. ∠r≅∠z b. (overline{tr}congoverline{xz})

Explanation:

Step1: Recall ASA congruence criterion

ASA (Angle - Side - Angle) states that two triangles are congruent if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.

Step2: Analyze given information

We can observe that we have one pair of congruent sides ($\overline{TS}\cong\overline{SZ}$). We need two pairs of angles where the given side is the included side for each triangle.

Step3: Determine required angle pair

We need $\angle R\cong\angle Z$ because then we would have two angles ($\angle R$ and $\angle Z$) and the included side ($\overline{TS}\cong\overline{SZ}$) for the two triangles $\triangle RTS$ and $\triangle XZS$ to satisfy ASA.

Answer:

A. $\angle R\cong\angle Z$