What is the procedure to draw a perpendicular bisector?

To draw a perpendicular bisector, use a compass and straightedge to find and connect the midpoint of a line segment.

First, start with the line segment you wish to bisect. Place the compass point on one end of the line segment and draw an arc above and below the line. Without changing the compass width, repeat this process from the other end of the line segment. You should now have two pairs of arcs that intersect above and below the line.

Next, use a straightedge to draw a line through the points where the arcs intersect. This line is the perpendicular bisector of the original line segment. It will cross the original line segment at a right angle (90 degrees) and divide it into two equal parts.

This method ensures accuracy because the arcs from the compass are equidistant from the endpoints of the line segment, guaranteeing that the bisector is both perpendicular and passes through the midpoint. This technique is fundamental in geometry and is often used in various constructions and proofs.