Ceva theorem

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A theorem on the relation between the lengths of certain lines intersecting a triangle. Let be three points lying, respectively, on the sides , and of a triangle . For the lines , and to intersect in a single point or to be all parallel it is necessary and sufficient that

Lines , and that meet in a single point and pass through the vertices of a triangle are called Ceva, or Cevian, lines. Ceva's theorem is metrically dual to the Menelaus theorem. It is named after G. Ceva [1].

Ceva's theorem can be generalized to the case of a polygon. Let a point be given in a planar polygon with an odd number of vertices , and suppose that the lines intersect the sides of the polygon opposite to respectively in points , . In this case


[1] G. Ceva, "De lineis rectis se invicem secantibus statica constructio" , Milano (1678)



[a1] M. Berger, "Geometry" , I , Springer (1987)
How to Cite This Entry:
Ceva theorem. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by P.S. Modenov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article