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.

Manipulative 1: Bisecting an angle. Created with GeoGebra. 
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.

Manipulative 3: Bisecting a Line Segment. Created with GeoGebra. 
Bisecting a Line Segment Using Analytical Geometry
 Figure 2: Bisecting a Line Segment 

Using analytical geometry, a line segment can be bisected. If the endpoints of
the line segment are (x_{1},y_{1}) and
(x_{2},y_{2}), then the midpoint of the
line segment is
((x_{1} + x_{2})/2,(y_{1} + y_{2})/2)
(see figure 2).

More Information
 McAdams, David. How to Bisect an Angle. allmathwords.org. Life is a Story Problem LLC. 20101015. 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. 20100108. http://www.allmathwords.org/article.aspx?lang=en&id=Bisecting a Line Segment.
Cite this article as:
Bisect. 20100108. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/b/bisect.html.
Translations
Image Credits
Revision History
20100108: Added "References" and "More Information" (
McAdams, David.)
20081024: Changed images and manipulatives to geogebra (
McAdams, David.)
20080507: Corrected link errors. Corrected spelling (
McAdams, David.)
20080422: Initial version (
McAdams, David.)