Bisect

Pronunciation: /baɪˈsɛkt/ ?

To bisect is to cut into two equal halves.[1] In geometry, bisecting an angle means divide the angle into two equal angles. Bisecting a line segment means dividing the line segment into two equal line segments.

Bisecting an Angle

Manipulative 1 shows how to construct the bisector of an angle.[2] Click on the blue point and drag it to change the figure. Click on the step check boxes one at a time to see the construction of an angle bisector. For more information on bisecting an angle, see How to Bisect an Angle.

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Manipulative 1: Bisecting an angle. Created with GeoGebra.
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Click on the blue points and drag them to change the figure.
Manipulative 2: Bisectors of a Triangle. Created with GeoGebra.

The angle bisectors of a triangle meet at the incenter of the triangle. See manipulative 2.

Bisecting a Line Segment

Manipulative 3 shows how to construct the midpoint and a bisector of a line segment.[2] Click on the blue points to change the figure. Click the check boxes to see how to bisect a line segment step by step.

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Manipulative 3: Bisecting a Line Segment. Created with GeoGebra.

Bisecting a Line Segment Using Analytical Geometry

A line with endpoints at (-2,3) and (4,-1) has a bisector at (1,1).
Figure 2: Bisecting a Line Segment

Using analytical geometry, a line segment can be bisected. If the endpoints of the line segment are (x1,y1) and (x2,y2), then the midpoint of the line segment is ((x1 + x2)/2,(y1 + y2)/2) (see figure 2).

More Information

  • McAdams, David. How to Bisect an Angle. allmathwords.org. Life is a Story Problem LLC. 2010-10-15. http://www.allmathwords.org/article.aspx?lang=en&id=How to Bisect an Angle.
  • McAdams, David. Bisecting a Line Segment. allmathwords.org. Life is a Story Problem LLC. 2010-01-08. http://www.allmathwords.org/article.aspx?lang=en&id=Bisecting a Line Segment.

Cite this article as:


Bisect. 2010-01-08. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/b/bisect.html.

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Revision History


2010-01-08: Added "References" and "More Information" (McAdams, David.)
2008-10-24: Changed images and manipulatives to geogebra (McAdams, David.)
2008-05-07: Corrected link errors. Corrected spelling (McAdams, David.)
2008-04-22: Initial version (McAdams, David.)

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