If `triangle ABC cong triangle DEF` then

Options

A. `AC=DE`
B. `BC=DF`
C. `FE=CB`
D. `AB=DF`

Answer

To solve the problem, we need to understand the concept of congruent triangles. When two triangles are congruent, it means that all their corresponding sides and angles are equal.

Given that triangle ABC is congruent to triangle DEF, we can denote this relationship as:

\[ \triangle ABC \cong \triangle DEF \]

### Step-by-Step Solution:

1. **Identify Corresponding Parts**:
Since the triangles are congruent, we can identify the corresponding sides and angles:
- Side AB corresponds to side DE
- Side BC corresponds to side EF
- Side AC corresponds to side DF
- Angle A corresponds to angle D
- Angle B corresponds to angle E
- Angle C corresponds to angle F

2. **Write the Equalities**:
Based on the congruence, we can write the following equalities:
- \( AB = DE \)
- \( BC = EF \)
- \( AC = DF \)

3. **Evaluate the Options**:
Now, we will evaluate the options provided in the question:
- **Option A**: \( AC = DE \) — This is incorrect because \( AC \) corresponds to \( DF \).
- **Option B**: \( BC = DF \) — This is incorrect because \( BC \) corresponds to \( EF \).
- **Option C**: \( EF = BC \) — This is correct as \( BC \) corresponds to \( EF \).
- **Option D**: \( AB = DF \) — This is incorrect because \( AB \) corresponds to \( DE \).

4. **Conclusion**:
The correct answer is **Option C**: \( EF = BC \).