Question

what else would need to be congruent to show that △abc≅ △xyz by asa? given: ∠x≅∠a ∠z≅∠c a. (overline{bc}congoverline{yz}) b. ∠z≅∠a c. (overline{ac}congoverline{xz}) d. ∠y≅∠c

Explanation:

Step1: Recall ASA congruence criterion

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

Step2: Identify given angles

We are given that $\angle X\cong\angle A$ and $\angle Z\cong\angle C$. The included sides for these pairs of angles are $\overline{AC}$ in $\triangle ABC$ and $\overline{XZ}$ in $\triangle XYZ$.

Step3: Determine the required congruence

For $\triangle ABC\cong\triangle XYZ$ by ASA, we need $\overline{AC}\cong\overline{XZ}$.

Answer:

C. $\overline{AC}\cong\overline{XZ}$