In geometry, a cevian is a line that intersects both a triangle's vertex, and also the side that is opposite to that vertex. Medians and angle bisectors are special cases of cevians. The name "Cevian" comes from the Italian mathematician Giovanni Ceva, who proved a well-known theorem about cevians which also bears his name.

Ceva's Theorem

Ceva's Theorem is the criteria for determining the congruence of cevians of a triangle. Cevians are line segments or rays that extend from a given vertex to the opposite side such as medians, altitudes, and angle bisectors. Cevians are not always found within the triangle.

The theorem states that in triangle ABC with points D, E, and F respectively on lines BC, CA, and AB, lines AD, BE, and CF are congruent if and only if the below ratios multiplied equal 1.