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The problem asks which congruence relationship proves that \( \triangle ECB \) is congruent. Here's the breakdown:

### Given Information:
1. Segments \( AB \cong ED \).
2. Segments \( BC \cong DC \).
3. The triangles \( \triangle ECB \) and \( \triangle EDB \) share angle \( \angle CEB \), making it congruent to itself by the **Reflexive Property**.

### Observations:
From the diagram and given information:
- Two pairs of sides are congruent (\( AB \cong ED \) and \( BC \cong DC \)).
- The included angle \( \angle CEB \) is congruent in both triangles.

### Conclusion:
This proves the triangles are congruent by **SAS (Side-Angle-Side)**, as two sides and the included angle are congruent in both triangles.

### Correct Answer: **SAS**

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### 5 Related Questions:
1. What does each congruence relationship (SAS, ASA, AAS, HL) mean in triangle congruence?
2. Why does the reflexive property of equality matter in proving triangle congruence?
3. How can overlapping triangles be analyzed using congruence rules?
4. What are the steps to prove triangles congruent using the SAS criterion?
5. How does "included angle" differ from other angles in a triangle?

### Tip:
Always look for shared sides or angles in overlapping triangles—they are often key to proving congruence.

Which of the following relationships proves why ΔECB are congruent? The diagram shows overlapping triangles, with segments AB ≅ ED and BC ≅ DC. The triangles share angle ∠CEB.

Understand how to prove ΔECB is congruent using the SAS congruence theorem. Learn about key concepts like the reflexive property, overlapping triangles, and congruence postulates, suitable for Grades 8-10.

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