Bisecting a Line Segment

Pronunciation: /baɪˈsɛkt ng eɪ laɪn/ Explain

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
1Line segment ABStart with line segment AB.
2Line segment AB with circle with center at A and edge at B.Draw a circle with center at A and edge at B.
3Line segment AB with circle with center at B and edge at A.Draw a circle with center at B and edge at A.
4Line segment AB with intersections of two circles marked C and D.Label the intersections of two circles as C and D.
5Line segment AB with line CD drawn.Draw line CD. This is the bisector of the line segment.
6Line segment AB intersection of AB and CD marked as E.Label the intersection of AB and CD as point E. This is the midpoint of points A and B.

Check Mark Understanding Check

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



Follow the instructions above to bisect the line segment.
Manipulative 1 - How to Bisect a Line Segment Using Geogebra Created with GeoGebra.
  1. Click on the circle from two points menu button GeoGebra circle with center through 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 Geogebra point menu button. to open the point constructor menu. Select the Intersect Two Objects Geogebra intersect two objects menu button 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 Geogebra line from two points menu button. 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 Geogebra intersect two objects menu button 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 GeoGebra arrow button. 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. Merriam-Webster. Last Accessed 6/19/2018. http://www.merriam-webster.com/dictionary/bisect.
  2. Council of Public Instruction for Upper Ireland. A Treatise on Mesuration for the use of Schools. pg 7. www.archive.org. Thom, Alexander. 1874. Last Accessed 6/19/2018. http://www.archive.org/stream/treatiseonmensur00ireluoft#page/7/mode/1up/search/bisect. Buy the book

More Information

  • McAdams, David E.. Bisect. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/22/2018. http://www.allmathwords.org/en/b/bisect.html.

Cite this article as:

McAdams, David E. Bisecting a Line Segment. 7/10/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/b/bisectingalinesegment.html.

Image Credits

Revision History

6/22/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
1/8/2010: Added "References" and "More Information". (McAdams, David E.)
7/5/2008: Initial version. (McAdams, David E.)

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