How to Bisect a Line Segment

Geometrical construction helps to make geometry more intuitive.

Bisecting a segment is one of the most fundamental operations in geometrical construction. Although simple in itself, bisecting is a procedure that a student will use over and over again in conjunction with other simple procedures. Combining these operations together paves the way for much more complex constructions. Apart from whatever practical applications geometrical construction may have, it challenges students to demonstrate their understanding of the principles of geometry, and the hands-on procedures help to make those principles more intuitive.

Things You'll Need

• Compass
• Straightedge

Instructions

1. Set the width of a compass so that it is about 3/4 of the length of the segment that you want to bisect.

2. Place the compass point on one of the endpoints, and draw two arcs on either side of the segment. Imagine a perpendicular line passing through the midpoint of the line segment and draw the arcs such that they intersect the imaginary line at two points.

3. Place the compass point on the other endpoint, and draw two arcs such that they intersect the two arcs that you just drew. If the first two arcs weren't big enough to form an intersection, go back and make them larger.

4. Line up a straightedge with the two intersection points and mark the point where the straightedge intersects the line segment. This midpoint bisects the segment.

References

• North Virginia Community College: To Bisect a Given Line Segment
• Massachusetts Institute of Technology: How to Bisect a Line