Menelaus’s Theorem

Pronunciation: /ˌmɛn.ɪˈleɪ.əs ˈθɪər.əm/ Explain

Menelaus’s theorem relates the way two cevians of a triangle divide each other and the sides of a triangle. Menelaus’s theorem is named for Menelaus of Alexandria.

Stated mathematically, Menelaus's theorem claims that, given triangle ABC, and a transversal line that crosses the extended sides of BC, AC, and AB at points D, E, and F respectively, with D, E, and F distinct from A, B, and C, then Or, stated another way:

Click on the blue points on the triangle and on the transversal and drag them to change the figure.

If the transversal does not cross the triangle, does the formula still hold true.
Manipulative 1 - Menelaus's Theorem Created with GeoGebra.

It is important to know that this theorem uses signed lengths of segments. Any segment that goes from left to right is positive. Any segment that goes from right to left is negative. Maniplulative 2 demonstrates positive and negative line segments.

Click on the blue points and drag them to change the figure.

Does the signed length AB always have the opposite signed of the signed length BA? Why?
Manipulative 2 - Signed Segment Length Created with GeoGebra.


  1. McAdams, David E.. All Math Words Dictionary, menelaus’s theorem. 2nd Classroom edition 20150108-4799968. pg 116. Life is a Story Problem LLC. January 8, 2015. Buy the book

Cite this article as:

McAdams, David E. Menelaus’s Theorem. 4/25/2019. All Math Words Encyclopedia. Life is a Story Problem LLC.

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Revision History

4/25/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
9/3/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
7/18/2018: Changed title to common format. (McAdams, David E.)
5/5/2011: Initial version. (McAdams, David E.)

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