WOLFRAM

Wolfram Language & System Documentation Center

AngleBisector[{q1,p,q2}]

gives the bisector of the interior angle at p formed by the triangle with vertex points p, q1 and q2.

AngleBisector[{q1,p,q2},"type"]

gives the angle bisector of the specified type.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Properties & Relations  
Possible Issues  
See Also
Related Guides
History
Cite this Page

AngleBisector

AngleBisector[{q1,p,q2}]

gives the bisector of the interior angle at p formed by the triangle with vertex points p, q1 and q2.

AngleBisector[{q1,p,q2},"type"]

gives the angle bisector of the specified type.

Details

Examples

open all close all

Basic Examples  (1)

Calculate an angle bisector:

Wolfram Language code: bisector = AngleBisector[{{1, 0}, {0, 0}, {1, Sqrt[3]}}]
Wolfram Language code: Graphics[{Arrow[{{0, 0}, {1, 0}}], Arrow[{{0, 0}, {1, Sqrt[3]}}], bisector}]

Scope  (2)

Find an interior angle bisector:

Wolfram Language code: AngleBisector[{{1, 0}, {0, 0}, {1, Sqrt[3]}}, "Interior"]

Find an exterior angle bisector:

Wolfram Language code: AngleBisector[{{1, 0}, {0, 0}, {1, Sqrt[3]}}, "Exterior"]

Properties & Relations  (4)

AngleBisector finds the interior angle bisector by default:

Wolfram Language code: AngleBisector[{{1, 0}, {0, 0}, {1, Sqrt[3]}}]
Wolfram Language code: AngleBisector[{{1, 0}, {0, 0}, {1, Sqrt[3]}}, "Interior"]

The angle bisector divides the angle into two equal angles:

Wolfram Language code: bisector = AngleBisector[{{1, 0}, {0, 0}, {1, Sqrt[3]}}]
Wolfram Language code: Graphics[{Arrow[{{0, 0}, {1, 0}}], Arrow[{{0, 0}, {1, Sqrt[3]}}], bisector}]
Wolfram Language code: PlanarAngle[{{1, 0}, {0, 0}, {3 / 2, Sqrt[3] / 2}}]
Wolfram Language code: PlanarAngle[{{3 / 2, Sqrt[3] / 2}, {0, 0}, {1, Sqrt[3]}}]

The exterior angle bisector divides the exterior angle into two equal angles:

Wolfram Language code: bisector = AngleBisector[{{1, 0}, {0, 0}, {1, Sqrt[3]}}, "Exterior"]
Wolfram Language code: Graphics[{Arrow[{{0, 0}, {1, 0}}], Style[Arrow[{{0, 0}, {-1, 0}}], Dashed], Arrow[{{0, 0}, {1, Sqrt[3]}}], bisector}]
Wolfram Language code: PlanarAngle[{{-1, 0}, {0, 0}, {-1 / 2, Sqrt[3] / 2}}]
Wolfram Language code: PlanarAngle[{{-1 / 2, Sqrt[3] / 2}, {0, 0}, {1, Sqrt[3]}}]

TriangleConstruct[{a,b,c},"AngleBisector"] is equivalent to AngleBisector[{a,b,c}]:

Wolfram Language code: TriangleConstruct[{{1, 0}, {0, 0}, {Sqrt[3], 1}}, "AngleBisector"]
Wolfram Language code: AngleBisector[{{1, 0}, {0, 0}, {Sqrt[3], 1}}]

Possible Issues  (2)

The three points must be distinct:

Wolfram Language code: AngleBisector[{{1, 0}, {0, 0}, {0, 0}}]

AngleBisector only works in 2D:

Wolfram Language code: AngleBisector[{{1, 0, 0}, {0, 0, 0}, {0, 0, 1}}]
Wolfram Research (2019), AngleBisector, Wolfram Language function, https://reference.wolfram.com/language/ref/AngleBisector.html.

Text

Wolfram Research (2019), AngleBisector, Wolfram Language function, https://reference.wolfram.com/language/ref/AngleBisector.html.

CMS

Wolfram Language. 2019. "AngleBisector." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AngleBisector.html.

APA

Wolfram Language. (2019). AngleBisector. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AngleBisector.html

BibTeX

@misc{reference.wolfram_2026_anglebisector, author="Wolfram Research", title="{AngleBisector}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/AngleBisector.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_anglebisector, organization={Wolfram Research}, title={AngleBisector}, year={2019}, url={https://reference.wolfram.com/language/ref/AngleBisector.html}, note=[Accessed: 13-June-2026]}