In `angleABC` and `angleLMN`, AB = LM and BC = MN. Which of the following conditions can make the two triangles congruent ?

Options

A. `angleA = angleL`
B. `angleB = angleM`
C. `angleC = angleN`
D. All of these

Answer

To determine the conditions under which triangles \( \triangle ABC \) and \( \triangle LMN \) can be congruent, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Information**:
- We know that \( AB = LM \) and \( BC = MN \).
- These represent two sides of each triangle.

2. **Draw the Triangles**:
- Draw triangle \( ABC \) with sides \( AB \) and \( BC \).
- Draw triangle \( LMN \) with sides \( LM \) and \( MN \).

3. **List the Known Sides**:
- From the problem, we have:
- \( AB = LM \) (first side)
- \( BC = MN \) (second side)

4. **Determine the Missing Information**:
- To establish congruence between two triangles, we need to know about the angles as well.
- We already have two sides, but we need to find the angle that is included between these two sides.

5. **Identify the Angle**:
- The angle that is included between the sides \( AB \) and \( BC \) in triangle \( ABC \) is angle \( B \).
- Similarly, the angle included between sides \( LM \) and \( MN \) in triangle \( LMN \) is angle \( M \).

6. **Set Up the Congruence Condition**:
- For the triangles to be congruent, we need:
- \( AB = LM \)
- \( BC = MN \)
- \( \angle B = \angle M \)

7. **Apply the SAS Congruence Criterion**:
- The condition we have is two sides and the included angle (SAS).
- Therefore, by the SAS (Side-Angle-Side) criterion, we can conclude that:
\[ \triangle ABC \cong \triangle LMN \]

### Conclusion:
The condition that can make the two triangles congruent is:
- \( \angle B = \angle M \).