1. **Problem Statement:** We are given the congruency statements between two triangles: $\overline{BC} \cong \overline{YZ}$, $\angle B \cong \angle Y$, and $\overline{AB} \cong \overline{XY}$. We need to identify which triangle congruency theorem applies and write the congruency statement for the triangles. 2. **Understanding the Given Information:** The congruent parts are two sides and the included angle between them: side $BC$, angle $B$, and side $AB$ correspond to side $YZ$, angle $Y$, and side $XY$ respectively. 3. **Relevant Triangle Congruency Theorems:** - Side-Side-Side (SSS): All three sides are congruent. - Side-Angle-Side (SAS): Two sides and the included angle are congruent. - Angle-Side-Angle (ASA): Two angles and the included side are congruent. - Angle-Angle-Side (AAS): Two angles and a non-included side are congruent. 4. **Applying the Theorem:** Since the given congruent parts are two sides and the included angle between them, the correct theorem is the Side-Angle-Side (SAS) Triangle Congruency Theorem. 5. **Writing the Congruency Statement:** The triangles are $\triangle ABC$ and $\triangle XYZ$, so the congruency statement is: $$\text{cong}(\triangle ABC, \triangle XYZ)$$ This means $\triangle ABC \cong \triangle XYZ$ by SAS. 6. **Summary:** The correct congruency theorem is Side-Angle-Side (SAS), and the congruency statement is $\text{cong}(\triangle ABC, \triangle XYZ)$.