For `triangle ABC cong triangle ACB`, then

Options

A. AB=AC
B. AB=BC
C. AC=BC
D. None of these

Answer

To solve the problem, we need to analyze the congruence of the two triangles given: triangle ABC and triangle ACB.

### Step-by-step Solution:

1. **Understand Triangle Congruence**:
- When two triangles are congruent, it means that their corresponding sides and angles are equal.

2. **Identify the Triangles**:
- We have triangle ABC and triangle ACB. The letters indicate the vertices of the triangles.

3. **Corresponding Sides**:
- For triangle ABC:
- Side AB corresponds to side AC.
- Side BC corresponds to side CB.
- Side AC corresponds to side AB.
- Therefore, we can establish the following equalities:
- AB = AC
- BC = CB (which is the same side)
- AC = AB

4. **Corresponding Angles**:
- The angles of the triangles also correspond as follows:
- Angle A (in triangle ABC) corresponds to Angle A (in triangle ACB).
- Angle B (in triangle ABC) corresponds to Angle C (in triangle ACB).
- Angle C (in triangle ABC) corresponds to Angle B (in triangle ACB).
- Thus, we have:
- Angle A = Angle A
- Angle B = Angle C
- Angle C = Angle B

5. **Evaluating the Options**:
- Now, we need to evaluate the options provided in the question:
- **Option 1**: AB = AC (This is correct as established).
- **Option 2**: AB = BC (This is incorrect since BC = CB, not equal to AB).
- **Option 3**: AC = BC (This is incorrect since BC = CB, not equal to AC).
- **Option 4**: None of these (This is incorrect since Option 1 is correct).

6. **Conclusion**:
- The correct option is **Option 1: AB = AC**.