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From the given image, you have two triangles labeled as \( \triangle ABC \) and \( \triangle DCB \), with the congruency statement \( \triangle ABC \cong \triangle DCB \).

To answer the question:

### 1. Corresponding Angles:
In congruent triangles, the corresponding angles are equal. Therefore:
- \( \angle A \) corresponds to \( \angle D \)
- \( \angle B \) corresponds to \( \angle B \) (they are the same angle)
- \( \angle C \) corresponds to \( \angle C \) (they are the same angle)

### 2. Corresponding Sides:
In congruent triangles, the corresponding sides are also equal. Therefore:
- \( \overline{AB} \) corresponds to \( \overline{DC} \)
- \( \overline{BC} \) corresponds to \( \overline{BC} \) (they are the same side)
- \( \overline{AC} \) corresponds to \( \overline{DB} \)

### 3. New Triangle Congruency Statement:
The new congruency statement could simply be the reverse order of the given statement, which is:
\[ \triangle DCB \cong \triangle ABC \]

Would you like further details on any of the corresponding parts or congruence criteria?

Here are some related questions:
1. What are the criteria for proving triangle congruence (e.g., SAS, SSS)?
2. Can two triangles be congruent if only two angles are equal?
3. How does the transitive property apply to congruent triangles?
4. What is the difference between congruent and similar triangles?
5. How would this triangle congruence affect any geometric properties (e.g., area, perimeter)?

**Tip:** When analyzing congruent triangles, always identify the corresponding angles and sides clearly to avoid confusion.

List corresponding angles, corresponding sides, and write a new triangle congruency statement. Given: ΔABC ≅ ΔDCB

Learn how to identify corresponding angles and sides in congruent triangles with this example where ΔABC ≅ ΔDCB. Understand the properties of triangle congruence and how to rewrite congruency statements, suitable for students in Grades 8-10.

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