Construction of a Perpendicular Bisector

Perpendicular Bisector

The line \(XY\) bisects \(AB\) when \(XY\) divides \(AB\) into two equal parts. \(M\) is a midpoint of the line segment \(AB\), and the line \(XY\) passes through point \(M\).

\(XY\) bisects \(AB\)

If the line \(XY\) bisects \(AB\) and \(XY\) is perpendicular to \(AB\), then \(XY\) is the perpendicular bisector of \(AB\).

Any point on the perpendicular bisector of a line segment is equidistant from two endpoints of the line segment.

\(XY\) bisects \(AB\) perpendicularly

Steps of Drawing Perpendicular Bisector

1. Draw the line segment.
2. Adjust the compass to slightly longer than half of the line segment.
3. Draw arcs above and below the line from one end of the line segment.
4. Use the same radius (do not adjust your compass) and draw arcs from the other end of line segment.
5. Where the arcs cross, join them with a line segment.