Table of Contents

 

Definition of the angle bisector

How to construct the angle bisector of a triangle

The formulas for the length of the angle bisector

The angle bisector and the opposite side of a triangle

The angle bisector divides the side of the triangle into line segments. The formula for the lengths of the line segments

The relationship between the three angle bisectors of a triangle

The angle bisector, the median and the height in a scalene triangle

Relationship between the angle bisector and the height in a triangle

The lemma of a three-leafed figure (relationship between the angle bisector, the inscribed circle and the circumscribed circle in a triangle) or the property of the extension of the angle bisector and the circumscribed circle

 

 

The intersection of the angle bisectors in a triangle

 

The intersection of the angle bisectors in a triangle. Properties

The line segments formed by intersection of the angle bisectors of a triangle

The distance from the vertex to the incenter. Formulas

The property of the line segment parallel to a side of the triangle and passing through the point of intersection of the angle bisectors

 

 

The bisectors of the exterior angles of a triangle. Properties

 

The bisectors of the exterior angles of a triangle. Properties

The properties of the bisector of the exterior and interior angles of a triangle

The properties of the exterior angle bisectors and the escribed circles of a triangle. The triangle of the exterior angle bisectors