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.