Question

determine if the triangles are congruent. if yes select correct congruence theorem. if no select not congruent. theorem select congruent select

Explanation:

Step1: Identify equal - sides

We see that $AB = XZ$, $BC=ZY$, $AC = XY$ as indicated by the tick - marks.

Step2: Apply congruence theorem

The Side - Side - Side (SSS) congruence theorem states that if three sides of one triangle are equal to three corresponding sides of another triangle, the two triangles are congruent. Since $AB = XZ$, $BC = ZY$, and $AC=XY$, $\triangle ABC\cong\triangle XZY$ by SSS.

Answer:

Congruent, SSS