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
StatementIn 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 YearDated to Euclid's Elements, traditionally placed circa 300 BCE; no more precise proof date is otherwise fixed. Classification
Statement Form Connections
Has Statement Form
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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 FoundationHistory 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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