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 .
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
|||G. Ceva, "De lineis rectis se invicem secantibus statica constructio" , Milano (1678)|
|[a1]||M. Berger, "Geometry" , I , Springer (1987)|
Ceva theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Ceva_theorem&oldid=17362