# Ceva theorem

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

#### References

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

#### Comments

#### References

[a1] | M. Berger, "Geometry" , I , Springer (1987) |

**How to Cite This Entry:**

Ceva theorem.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Ceva_theorem&oldid=17362