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The question asks: If \(\triangle ABC \cong \triangle XYZ\), which statement is always true?

When two triangles are congruent (\(\cong\)), all corresponding sides and angles are equal. This means the corresponding sides of \(\triangle ABC\) and \(\triangle XYZ\) are equal in length, and the corresponding angles are equal in measure.

Let’s analyze each of the answer choices:

1. **AC = XY** – This is incorrect. The sides AC and XY are not corresponding sides. Instead, AC corresponds to XZ.
2. **\(\angle B \cong \angle C\)** – This is incorrect. Angles \(\angle B\) and \(\angle C\) are both from the same triangle, but they are not corresponding angles between the two triangles.
3. **AB = YZ** – This is incorrect. AB corresponds to side XY, not YZ.
4. **\(\angle C \cong \angle Z\)** – This is the correct answer. \(\angle C\) and \(\angle Z\) are corresponding angles between the two congruent triangles.

Therefore, the correct answer is: **\(\angle C \cong \angle Z\)**.

Would you like more details or have any questions about triangle congruence?

Here are 5 follow-up questions you could explore:
1. How do you determine corresponding sides in congruent triangles?
2. What are the different criteria to prove triangle congruence?
3. Why is it important for corresponding angles to be congruent?
4. Can two triangles be congruent if only two pairs of sides are equal?
5. How do you apply the concept of triangle congruence to solve real-world problems?

**Tip**: When identifying corresponding parts in congruent triangles, always match the order of the vertices carefully (e.g., \(\triangle ABC \cong \triangle XYZ\)).

If ∆ABC ≅ ∆XYZ, which statement is always true?

Explore which statements are always true for congruent triangles ∆ABC ≅ ∆XYZ. Understand the relationships between corresponding angles and sides using the concept of triangle congruence and CPCTC. Suitable for students in Grades 8-10.

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