CK-12 Geometry-Concepts

5.3. Angle Bisectors in Triangles http://www.ck12.org

MEDIA

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URL: http://www.ck12.org/flx/render/embeddedobject/1288

James Sousa: Proof of the Angle Bisector Theorem

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URL: http://www.ck12.org/flx/render/embeddedobject/1289

James Sousa: Proof of the Angle Bisector Theorem Converse

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URL: http://www.ck12.org/flx/render/embeddedobject/1290

James Sousa: Solving For Unknown Values Using Angle Bisectors

Guidance

Recall that anangle bisectorcuts an angle exactly in half. Let’s analyze this figure.

−→

BDis the angle bisector of^6 ABC. Looking at pointD, if we were to drawEDandDF, we would find that they are
equal. Recall that the shortest distance from a point to a line is the perpendicular length between them.EDandDF
are the shortest lengths betweenD,which is on the angle bisector, and each side of the angle.

Angle Bisector Theorem:If a point is on the bisector of an angle, then the point is equidistant from the sides of the
angle.

In other words, if

←→

BDbisects^6 ABC,

−→

BE⊥ED, and

−→

BF⊥DF, thenED=DF.