Bisector
A bisector is something that cuts an object into two equal parts. It is applied to angles and line segments.
In verb form, we say that it bisects the other object.
1. Angle bisector
A line that cuts an angle into two equal parts.
In the figure below the blue line bisects the angle LJM. The blue line is the bisector.
For more on this see Angle bisector.
2. Line segment bisector
A line which cuts another line segment into two equal parts.
In the figure below, the line segment AB is the bisector. It bisects the line PQ  dividing it into two equal parts.
For more on this see Line bisector.
Definition of 'Angle Bisector' and a general discussion of bisection. Link to 'line bisector'
This construction shows how to draw the perpendicular bisector of a given line segment with compass and straightedge or ruler. This both bisects the segment (divides it into two equal parts), and is perpendicular to it. Finds the midpoint of a line segmrnt. The proof shown below shows that it works by creating 4 congruent triangles. A Euclideamn construction.
How to bisect an angle with compass and straightedge or ruler. To bisect an angle means that we divide the angle into two equal (congruent) parts without actually measuring the angle. This Euclidean construction works by creating two congruent triangles. See the proof below for more on this.
Definition of 'Line Bisector' and a general discussion of bisection. Link to 'angle bisector'
Definition of 'Perpendicular Bisector'
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