The line segment connecting the midpoints of two sides of a triangle is called the midline of the triangle.

Triangle midline theorem: the midline of a triangle is parallel to the third side and equal to half of the third side.

Theorem for determining the midline of a triangle: A straight line parallel to the second side will bisect the third side after passing through the midpoint of one side of the triangle.

Midpoint:

The point where a line segment is divided into two equal line segments is called the midpoint of this line segment. Judgments and theorems are all in it.

High:

If a vertical line is drawn from the vertex of a triangle to its opposite side (or the straight line where the opposite side is located), then the line segment between the vertex and the vertical foot is called the height line of the triangle, which is called height for short.

Judgment: A line segment perpendicular to the opposite side with a vertex of a triangle as the endpoint.

Theorem: The height of a triangle is perpendicular to one side of the triangle, and its endpoint is a vertex of the triangle.

Angular bisector:

Draw a ray from the vertex of an angle and divide it into two identical angles. This ray is called the bisector of this angle.

Judgment: The set of points with equal distance to both sides of the angle constitutes the bisector of the angle.

Theorem: A point on the bisector of an angle is equal to the distance on both sides of the angle.

Perpendicular bisector:

A straight line that passes through the midpoint of a line segment and is perpendicular to the line segment is called the midline of the line segment.

Judgment: The set of points with the same distance from both ends of the line segment constitutes the median vertical line of the line segment.

Theorem: The distance between the point on the vertical line of a line segment and the two endpoints of this line segment is equal.