It appears you have a mathematical assignment involving triangle properties. Here's a brief summary of the tasks included:

### Bài 4 (Problem 4):
Given triangle \( ABC \) with \( AB = AC \) and point \( H \) as the midpoint of side \( BC \).

a) Prove that triangles \( \triangle ABH \) and \( \triangle ACH \) are congruent and that \( AH \) is perpendicular to \( BC \).

b) Show that two altitudes through points \( M \) and \( N \), originating from points \( B \) and \( C \) respectively, lead to the conclusion that triangles \( \triangle AHM \) and \( \triangle AHN \) are congruent.

c) Point \( I \) is the midpoint of side \( NC \). Draw a line from point \( C \) parallel to line \( HN \) that intersects \( HI \) at point \( K \). Prove that \( NK \parallel HC \) and that points \( M \), \( N \), \( K \) are collinear.

### Bài 5 (Problem 5):
Given triangle \( ABC \) with \( AB < AC \), where point \( D \) is the midpoint of side \( AC \). Based on a line \( DB \), identify point \( E \) such that \( DB = DE \).

a) Prove that triangles \( \triangle ADB \) and \( \triangle CDE \) are congruent.

b) Draw segment \( BD \) and extend to \( E \). Show that \( CF \) intersects \( DE \) at point \( G \) and prove the respective triangles are congruent.

c) For a line segment from point \( C \) leading to point \( D \), demonstrate that it intersects segment \( BH \) and prove a specified relation among triangles formed by these intersections.

If you need further explanation or help on any specific part, feel free to ask!