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The missing reason in step 2, where you are stating that \( CD \cong CD \), is known as the **Reflexive Property of Congruence**. This property states that any geometric figure (in this case, segment \( CD \)) is congruent to itself.

### Updated reasoning for step 2:

- **Statement:** \( CD \cong CD \)
- **Reason:** Reflexive Property of Congruence

Would you like me to explain further steps in the proof or dive deeper into this problem?

Here are 5 related questions:
1. What is the significance of the reflexive property in geometric proofs?
2. How does the SAS (Side-Angle-Side) congruence criterion apply to this problem?
3. What other properties of congruence are commonly used in geometric proofs?
4. Why is it important to establish that \( AB \parallel EF \)?
5. Can triangle congruence alone prove lines are parallel, or do we need additional theorems?

**Tip:** Always check for shared sides or angles between triangles, as reflexive properties or vertical angles can be crucial in many geometric proofs.

Prove AB || EF given BD ≅ CE, ∠ACB ≅ ∠FDE, and AC ≅ FD.

In this geometry problem, learn how to prove that AB is parallel to EF using the given congruences of triangles and the Reflexive Property of Congruence. This proof applies the SAS criterion and geometric properties related to parallel lines. Ideal for students in Grades 9-11.

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