The theorem of angular bisector 1 is a theorem describing the quantitative relationship between the distance between a point on the angular bisector and both sides of the angle, and can also be regarded as the nature of the angular bisector.

Theorem 2 of angular bisector is a theorem of equal proportion of line segments obtained by putting angular bisector into triangle. From it and related formulas, the quantitative relationship between the length of bisector of triangle inner angle and each line segment can be deduced.

The ray from the vertex of an angle that divides the angle into two equal angles is called the bisector of the angle. The line segment formed by the intersection of the bisector of an angle (inner angle) of a triangle and the point on its opposite side is called the bisector of this triangle.

As follows:

Definition of triangle. The bisector of an angle of a triangle intersects the opposite side of the angle, and the line segment connecting the vertex of the angle and the opposite side is called the bisector of the triangle (also called the bisector of the inner angle of the triangle). By definition, the bisector of a triangle is a line segment. Because a triangle has three internal angles, it has three bisectors. The intersection of the bisectors of a triangle must be inside the triangle.

In geometry, an angle is a geometric object composed of two rays with a common endpoint. These two rays are called the edges of an angle, and their common endpoint is called the vertex of the angle. The general angle is assumed to be in Euclidean plane, but it can also be defined in Euclidean geometry. Angle is widely used in geometry and trigonometry.

Euclid, the father of geometry, once defined an angle as the relative inclination of two non-parallel straight lines in a plane. Proclos thinks that angle may be a trait, a quantifiable quantity, or a relationship. Oldham thinks that an angle is a deviation from a straight line, and Cabus of Antioch thinks that an angle is a space between two intersecting straight lines. Euclid thinks that an angle is a relationship, but its definitions of right angle, acute angle and obtuse angle are quantitative.

The figure formed by the rotation of light from one position to another around its endpoint is called an angle. The endpoint of the rotated ray is called the vertex of the angle, the ray at the starting position is called the starting edge of the angle, and the ray at the ending position is called the ending edge of the angle. Significance: In order to eliminate the limitation of operation and break through the angle range.