Perpendicular Bisector is a straight line passing through the midpoint of the line segment and perpendicular to it.
Properties of Perpendicular Bisector:
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 .
To draw the perpendicular bisector of the line segment using compass, we follow the following steps:
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).
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 ).
At the last step, we connect the intersection of the arches on the upper and lower sides by a straight line.
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 three perpendicular bisectors intersect at a one point, this point being the center of a circle circumscribed to triangle .