https://file.aiquickdraw.com/mathbot/file/1729254116780zbpa8crh.jpg

Let's analyze the problem and its components. The question is asking to complete a congruence statement for the two triangles shown in the image, \( \triangle ABC \) and \( \triangle DEF \). 

### Step-by-Step Solution:

1. **Identify Corresponding Angles and Sides**:
   - In \( \triangle ABC \), angle \( B \) is marked with a small circle at the top, which corresponds to angle \( E \) in \( \triangle DEF \).
   - Sides \( AB \) and \( BC \) are marked as congruent to sides \( DE \) and \( EF \), respectively.

2. **Congruence Postulate**:
   - We are given two sides and an included angle that are congruent between the triangles. This matches the criteria for the **SAS (Side-Angle-Side) Congruence Postulate**.

3. **Congruence Statement**:
   - Since angle \( B \) corresponds to angle \( E \), and the sides around these angles are congruent, the correct congruence statement is:
   \[
   \triangle ABC \cong \triangle DEF \quad \text{by the SAS postulate.}
   \]

### Final Answer:
- \( \triangle ABC \cong \triangle DEF \) by the **SAS (Side-Angle-Side) Congruence Postulate**.

Would you like further details or clarifications?

### Relative Questions:
1. How do you determine which congruence postulate applies?
2. What are the key differences between SSS, SAS, and ASA postulates?
3. How do we identify corresponding parts of congruent triangles?
4. What other scenarios might use the ASA (Angle-Side-Angle) postulate?
5. How can you prove triangle similarity instead of congruence?

### Tip:
When dealing with triangle congruence, always identify corresponding parts (angles and sides) before deciding which postulate applies.

Use the image to complete the congruence statement: △ABC ≅ ? by the ? congruence postulate.

This problem involves completing a triangle congruence statement using the SAS postulate. Learn how to identify corresponding sides and angles in triangles ABC and DEF, and use the SAS postulate to determine congruence.

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