Cho △ABC có AB < AC, AE là tia phân giác của BAC. Lấy M thuộc AC, AM = AB

The equations and statements on the chalkboard are problems in geometry, specifically related to triangle properties. Here is a summary of the content:

### Problem 3 (BT3):
1. Given triangle \( \triangle ABC \) with \( AB < AC \) and \( AE \) as the angle bisector of \( \angle BAC \). Take \( M \) on \( AC \) such that \( AM = AB \).
- a) Prove \( \triangle ABE \cong \triangle AMC \).
- b) \( AE \cap BM \equiv I \). Prove \( IB = IM \).
- c) Construct \( N \) as the reflection of \( M \) across \( EM \), and \( EN = EC \).
- d) Prove that \( A, B, N \) are collinear.

### Problem 5 (BT5):
1. Given triangle \( \triangle ABC \) is isosceles at \( A \) with the center \( A_I \) of the incircle \( I \).
- a) Prove that \( IM = IN \) and \( AM = AN \).
- b) Prove \( MN \parallel BC \).

### Problem 6 (BT6):
1. Given triangle \( \triangle ABC \) is right-angled at \( A \), with \( A \) projecting onto the line \( BC \).
- a) Prove that \( \triangle BAD \cong \triangle ACE \).
- b) Prove \( DE = DB + CE \).

These problems involve congruence, angle bisectors, reflections, and properties of triangles. If you need detailed solutions or steps, let me know!