1. The problem states that triangle sides AB ≅ XY, BC ≅ YZ, and CA ≅ ZX are congruent. 2. To determine which triangle congruency theorem applies, recall the common theorems: - 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. - Side-Angle-Side (SAS): Two sides and the included angle are congruent. - Side-Side-Side (SSS): All three sides are congruent. 3. Since all three pairs of corresponding sides are congruent, the Side-Side-Side (SSS) Triangle Congruency Theorem applies. 4. Therefore, the congruency statement is: $$\text{cong}(\triangle ABC, \triangle XYZ)$$ This means triangle ABC is congruent to triangle XYZ by the SSS theorem.