Gives a ratio condition for three points, one on each side (or its extension) of a triangle, to be collinear. Attributed to Menelaus of Alexandria, it is a companion result to Ceva's theorem and a staple of classical triangle geometry.
Facts
StatementFor a triangle ABC crossed by a transversal line meeting BC, CA, and AB, or their extensions, at points D, E, and F, the signed ratios AF over FB, BD over DC, and CE over EA multiply to negative one. 1 Classification
Statement Form Connections
Has Statement Form
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.
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
Sources
1. Menelaus's Theorem (Wikipedia)
Wikimedia FoundationHistory sectionQuote, History section
It is uncertain who actually discovered the theorem; however, the oldest extant exposition appears in Spherics by Menelaus.
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