﻿ Bisecting a Line Segment: How to bisect a line segment with a compass and straight edge.

# Bisecting a Line Segment

Pronunciation: baɪˈsɛk tiŋ ə laɪn ˈsɛg mənt ?

To bisect is to cut into two equal parts. To bisect a line segment is to cut the line segment into two parts.[1]
StepExampleDescription
2Draw a circle with center at A and edge at B.
3Draw a circle with center at B and edge at A.
4Label the intersections of two circles as C and D.
5Draw line CD. This is the bisector of the line segment.
6Label the intersection of AB and CD as point E. This is the midpoint of points A and B.

#### Understanding Check

Use the GeoGebra application below to construct the bisector and midpoint of line segment AB.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)
1. Click on the circle from two points menu button . Click on point A then point B. This draws a circle with center at point A and edge at point B.
2. With the circle from two points menu button still selected, click on point B then on point A. This draws a circle with center at point B and edge at point A.
3. Click on the down arrow of the Point menu button to open the point constructor menu. Select the Intersect Two Objects menu button. Click on each of the two circles. Points C and D will appear at the intersections of the two circles.
4. Click on the Line from Two Points menu button. Then click on points C and D. This draws a line through points C and D. Line CD is the bisector of segment AB.
5. Click on the Intersect Two Objects menu button. Then click on line segment AB then line CD. Point E appears. Point E is the midpoint of points A and B.

To change the manipulative, first click on the arrow menu button. Then click on the blue points and drag them to change the figure.

Table 1: Bisecting a line segment.

### References

1. bisect. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2009-03-12). http://www.merriam-webster.com/dictionary/bisect.
2. A Treatise on Mesuration for the use of Schools, pg 7. Thom, Alexander, 1874. (Accessed: 2010-01-08). http://www.archive.org/stream/treatiseonmensur00ireluoft#page/7/mode/1up/search/bisect.

• McAdams, David. Bisect. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2010-01-08. https://www.allmathwords.org/article.aspx?lang=en&id=Bisect.

Bisecting a Line Segment. 2010-01-08. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/h/htbisectlineseg.html.