Perpendicular bisector

To bisect something means to cut it into two equal parts. The word is composed of bi- meaning two and a Latin word secare meaning to cut. A bisector is a line that cuts an angle or a line segment in two.

A perpendicular bisector is a line that cuts a line segment in two at 90 degrees to the line segment.

Here is a line segment

In order to cut it into two equal parts at , we can draw two circles with the same radius at each point on the line segment like this:

As long as the radii of the circles are greater than half the length of the line segment then the circles will cross at two points, one above and one below the line segment.

Drawing a line segment using a straight edge that passes through the two points where the circles cross bisects the line at .

Of course, when you construct a perpendicular bisector using a compass and straight edge, you don’t need to draw full circles, you can draw two arcs that overlap, like this: