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
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Source Menelaus's Theorem (Wikipedia)
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.
Menelaus's Theorem (Wikipedia)
Proved By: Menelaus of Alexandria, LeadQuote, Proved By: Menelaus of Alexandria, Lead
In Euclidean geometry, Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry
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