If for `∆ABC and ∆DEF`, the correspondence `CAB ↔ EDF` gives a congruence, then which of the following is not true?

Options

A. `AC=DE`
B. `AB=EF`
C. `angleA=angleD`
D. `angleC= angle E`

Answer

To solve the problem, we need to analyze the congruence of triangles \( \Delta ABC \) and \( \Delta DEF \) given the correspondence \( CAB \leftrightarrow EDF \). We will look at the properties of congruent triangles and determine which statement is not true.

### Step-by-Step Solution:

1. **Understanding Congruence**:
- When two triangles are congruent, it means that their corresponding sides and angles are equal.
- The notation \( CAB \leftrightarrow EDF \) indicates that:
- Angle \( C \) corresponds to angle \( E \)
- Angle \( A \) corresponds to angle \( D \)
- Angle \( B \) corresponds to angle \( F \)

2. **Corresponding Angles**:
- From the congruence, we have:
- \( \angle C = \angle E \)
- \( \angle A = \angle D \)
- \( \angle B = \angle F \)

3. **Corresponding Sides**:
- The sides corresponding to these angles are:
- Side \( AB \) corresponds to side \( DE \)
- Side \( BC \) corresponds to side \( EF \)
- Side \( CA \) corresponds to side \( FD \)

4. **Analyzing the Options**:
- We need to check the given options to find which one is not true.
- Let's denote the options as follows:
1. \( AC = DE \)
2. \( AB = FD \)
3. \( BC = EF \)
4. \( CA = FD \)

5. **Checking Each Option**:
- **Option 1**: \( AC = DE \) → This is true because \( AC \) corresponds to \( DE \).
- **Option 2**: \( AB = FD \) → This is not true because \( AB \) corresponds to \( DE \), not \( FD \).
- **Option 3**: \( BC = EF \) → This is true as \( BC \) corresponds to \( EF \).
- **Option 4**: \( CA = FD \) → This is true as \( CA \) corresponds to \( FD \).

6. **Conclusion**:
- The statement that is not true is **Option 2**: \( AB = FD \).

### Final Answer:
The option that is not true is **Option 2: \( AB = FD \)**.