Bisecting a Segment

To bisect a segment means to draw the object that bisects it, or passes through its midpoint.

Here, a bisector of AB will be constructed using a compass and a straightedge.

Draw an Arc Centered at A

Place a compass with its needle point at A. Set the compass to go beyond half the length of the segment. Then draw an arc that intersects the segment.

Draw an Arc Centered at B with the Same Radius

Keep the compass set to the same length. Then place the needle point at the other end of the segment and draw a second arc across the segment.

If the arcs have been drawn large enough, they will now intersect each other twice. If they don't, extend them.

Draw a Line Through the Points of Intersections of Arcs

Use the straightedge to draw a line through the intersection points of the arcs. The point where the line and the segment intersect is the midpoint of AB.

Bisectors of AB

Any line that passes through the midpoint of AB is a bisector of AB.

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