Δ ABC (AB < AC). Trên cạnh AC có điểm M trong miền BD. Yêu cầu Δ ABM = Δ ADM bởi

To tackle the problem with triangle \( \Delta ABC \) where \( AB < AC \) and point \( M \) lies on segment \( AC \), we will analyze it based on the provided statements.

### Given:
- \( \Delta ABC \) with \( AB < AC \).
- Point \( M \) lies on segment \( AC \) within region \( BD \).
- We need to establish that \( \Delta ABM \cong \Delta ADM \) (the two triangles are congruent).

### Steps to Prove \( \Delta ABM \cong \Delta ADM \):

1. **Congruent Triangles**:
- For triangles to be congruent, we can apply the criteria such as SSS, SAS, or AAS.

2. **Identifying Elements**:
- Let \( AM \) represent a common side in both triangles.
- \( AB \) and \( AD \) are given as congruent sides since \( AB = AD \) (both are equal in length).

3. **Common Angle**:
- \( \angle AMB = \angle AMD \). This is crucial as it shows that the angle formed at point \( M \) is the same for both triangles.

4. **Using Segment**:
- The segment lengths and the angles provide sufficient information for proving congruence.
- According to the information, since \( AM \) is involved in both triangles and the equality of the other sides, congruence can be established via the SAS (Side-Angle-Side) postulate.

5. **Conclusion**:
- Therefore, we can conclude that \( \Delta ABM \cong \Delta ADM \) by the SAS condition.

Make sure to verify that all conditions of congruency are fulfilled in a diagram for clarity and completeness. This will help clarify how the relationships among the sides and angles operate within the geometrical framework set by the problem.