Theorem

Angle Bisector Theorem

Geometry

In geometry, the angle bisector theorem concerns the relative lengths of the two segments that a triangle's side is divided into by a line bisecting the opposite angle. It equates those relative lengths to the relative lengths of the triangle's other two sides.

Facts

Statement

In a triangle, the bisector of an angle divides the opposite side into two segments whose lengths are in the same ratio as the lengths of the two sides adjacent to that angle. 1

Proof Year

300 BCE 1

Dated to Euclid's Elements, traditionally placed circa 300 BCE; no more precise proof date is otherwise fixed.

Classification

Statement Form

Identity or Equation 1

Connections

Has Statement Form

Equation

Identity

In Branch

Geometry

Source Angle Bisector Theorem (Wikipedia)

Proved By

Robert Simson

Source Angle Bisector Theorem (Wikipedia)

Sources

1. Angle Bisector Theorem (Wikipedia)

Wikimedia Foundation

History section, first sentence
The angle bisector theorem appears as Proposition 3 of Book VI in Euclid's Elements.
In Branch: Geometry, Lead sentence
In geometry, the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divid
Proved By: Robert Simson, Lead
According to Heath (1956, p. 197 (vol. 2)), the corresponding statement for an external angle bisector was given by Robert Simson who noted that Pappus assumed this result without proof

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Angle Bisector Theorem

Has Statement Form

In Branch

Proved By