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The question asks which postulate or theorem proves that triangles \( \triangle CFE \) and \( \triangle DFE \) are congruent. 

### Observations from the diagram:
- Both triangles share side \( \overline{FE} \) (common side).
- \( \overline{CF} \) and \( \overline{DF} \) are marked as congruent (they have equal length).
- \( \angle CFE \) and \( \angle DFE \) are marked as congruent (these angles have equal measure).

### Conclusion:
- We have two pairs of congruent sides (\( \overline{CF} = \overline{DF} \) and \( \overline{FE} \) shared), and the included angle between these sides is congruent (\( \angle CFE = \angle DFE \)).
  
This satisfies the **Side-Angle-Side (SAS) Congruence Postulate**.

Therefore, the correct answer is:
- **SAS Congruence Postulate**

Would you like more details on the reasoning, or do you have any other questions?

### 5 related questions:
1. What is the difference between the SAS and SSS congruence postulates?
2. How can we use the ASA postulate to prove triangle congruence?
3. What are some real-life applications of triangle congruence?
4. Can the AAS congruence theorem be applied if we know two angles and a non-included side?
5. How does the reflexive property help in proving triangle congruence?

### Tip:
When using postulates like SAS or SSS, always check for pairs of congruent sides or angles, and ensure the angles are included between the sides when using SAS.

Which postulate or theorem proves that ∆CFE and ∆DFE are congruent?

This problem involves determining the postulate that proves the congruence of triangles ∆CFE and ∆DFE. The solution uses the SAS Congruence Postulate, showing that two pairs of sides and the included angle are congruent. Suitable for students in Grades 8-10.

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