One method of proving this theorem involves setting the result of Routh's theorem equal to zero and rearranging, and the dual of this theorem involving collinearity is named for Menelaus.
One method of proving this theorem involves setting the result of Routh's theorem equal to zero and rearranging, and the dual of this theorem involving collinearity is named for Menelaus. Its usually proven by pairwise similarity using ratios of areas, and applying the law of Sines to it gives the useful "trig" version of this result. This theorem is used to prove the existence of the centroid from the properties of medians, and can also be used to show the existence of the incenter and circumcenter. For 10 points, name this theorem that gives a concurrency condition for lines extending from a vertex of a triangle to the opposite side.
One method of proving this theorem involves setting the result of Routh's theorem equal to zero and rearranging, and the dual of this theorem involving collinearity is named for Menelaus.
{Ceva}’s Theorem