Menelaus’ theorem

If the points X, Y and Z are on the sides of a triangle ABC (including their prolongations), collinearMathworldPlanetmath and do not coincide with any of the points A, B and C, then the equation


holds (all segments are directed line segments). The converse of this theorem also holds (thus: three points on the prolongations of the triangle’s sides are collinear if the above equation holds).

Title Menelaus’ theorem
Canonical name MenelausTheorem
Date of creation 2013-03-22 12:46:20
Last modified on 2013-03-22 12:46:20
Owner mathwizard (128)
Last modified by mathwizard (128)
Numerical id 7
Author mathwizard (128)
Entry type Theorem
Classification msc 51A05
Related topic CevasTheorem
Related topic TrigonometricVersionOfCevasTheorem
Related topic Collinear