Perpendicular Bisector: Bisector of a Line Segment

Perpendicular Bisector is a straight line passing through the midpoint of the line segment and perpendicular to it.

Properties of Perpendicular Bisector:

• Divides the line segment into two equal lines segments;
• Each point belongs to the bisector of the segment, so it is located at the same distance with the two endpoints of the segment;
• The Perpendicular Bisector of the segment forms two right angles at the midpoint;

In the following figure, we have the line and the median of the line segment , and we notice that two right angles formed at the midpoint .

How to draw a Perpendicular Bisector

To draw the perpendicular bisector of the line segment using compass, we follow the following steps:

Step1:

Draw an arc on the top side and an arc on the bottom side of a circle with center (endpoint of ) and radius so that (the radius should be a little bigger than the middle of the line segment).

Step2:

Without changing the radius which we took in step 1, draw an arc on the top side and an arc on the bottom side of a circle with center (endpoint of ).

Step3:

At the last step, we connect the intersection of the arches on the upper and lower sides by a straight line.

Perpendicular Bisectors of a Triangle

We saw that each segment had a perpendicular bisector. So a triangle that has three sides can have three perpendicular bisectors.

Following the same steps above, we draw the perpendicular bisectors of triangle below:

• The perpendicular bisector of
  

  
• The perpendicular bisector of
  

  
• The perpendicular bisector of
  

  

The three perpendicular bisectors intersect at a one point, this point being the center of a circle circumscribed to triangle .