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Angle bisector theorem - Wikipedia, the free encyclopedia

Angle bisector theorem

From Wikipedia, the free encyclopedia

In this diagram, BD:DC = AB:AC.
In this diagram, BD:DC = AB:AC.

In geometry, the angle bisector theorem relates the length of the side opposite one angle of a triangle to the lengths of the other two sides of the triangle.

Consider a triangle ABC. Let the angle bisector of angle A intersect side BC at a point D. The angle bisector theorem states that the ratio of the length of the line segment BD to the length of segment DC is equal to the ratio of the length of side AB to the length of side AC.

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