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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, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Identity, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

In Branch

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
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