Properties of a triangle with three concurrent Cevian lines

Abstract

Consider an ordinary triangle with three concurrent Cevian lines drawn from the three vertices. There are six lines altogether in the figure. We assert that the interior ratio within a line segment of all six lines can be easily determined given the interior ratio of any two lines. This is done through four theorems. The first two are the well‐known theorems of Menelaus and Ceva. The third and fourth theorems are less well known, but are presented in simple forms and can be considered as companion theorems to those of Menelaus and Ceva.