Segment and Angle Bisectors:

Segments

A line segment is a part of a line that has two endpoints. The two endpoints of the line segment are used to name the line segment. A line has no endpoints, therefore it cannot be measured. But a line segment has two endpoints and hence the length can be measured.

Types of line segments

There are so many types of segments according to their properties. Some line segments will meet at a point. So they are called intersecting line segments.

When three or more lines meet at the same point, they are called concurrent line segments.

When two line segments intersect to form a right angle, it is called perpendicular line segment.

Two line segments which do not intersect but are on the same plane are called parallel line segments.

Two line segments which cannot intersect as they are on the different planes are called skew line segment.

Two line segments which are of the same length are called congruent line segments.

Angle bisectors

An angle bisector in a triangle is a segment drawn from a vertex that bisects (cuts in half) that vertex angle. Every triangle has three angle bisectors. In every triangle, the three angle bisectors meet in one point inside the triangle.

For every angle, there exists a line that divides the angle into two equal parts. This line is known as the angle bisector. In a triangle, there are three such lines. Three angle bisectors of a triangle meet at a point called the incenter of the triangle.

In general, altitudes, medians, and angle bisectors are different segments. In certain triangles, though, they can be the same segments. The altitude drawn from the vertex angle of an isosceles triangle can be proven to be a median as well as an angle bisector.

Angle Bisector Postulate states that there exists only one angle bisector with each angle.
Any point on an angle bisector is equidistant from both the arms of the angle.