You can use a compass to bisect an angle or a line segment.

• For a line segment, open the compass to a bit more than half the line segment’s length (visually, not by measuring).
• Place the needle on one endpoint and swing an arc above and below the line segment.
• Relocate the compass to the other end of the line segment and repeat the swing.
• The points where the two arcs intersect above and below the line segment are the two points to connect with your straightedge.
• That straight, perpendicular line will bisect the line segment!

Midpoints and perpendicular bisectors

Construct a midpoint and a perpendicular bisector for line segment AB as given below:

Step 1: Place the compass point on point A and open the compass such that its width is greater than half the length
of the line segment. Maintain the width of the compass and draw an arc above and below the line segment. Keep in mind that the arc will need to intersect the arc drawn in the next step, so draw arc that are relatively long.

Step 2: Maintain the compass width, place the compass point on B, and draw arc above and below the line segment such that they intersect the first arc at two points.

Step 3: Draw a line through the intersections of the two arcs. Call the point of intersection of the line and line segment
AB point C. Point C is the midpoint and the line is the perpendicular bisector of line segment AB.