Affine geometry | Area | Theorems about triangles
Routh's theorem
In geometry, Routh's theorem determines the ratio of areas between a given triangle and a triangle formed by the pairwise intersections of three cevians. The theorem states that if in triangle points , , and lie on segments , , and , then writing , , and , the signed area of the triangle formed by the cevians , , and is the area of triangle times This theorem was given by Edward John Routh on page 82 of his Treatise on Analytical Statics with Numerous Examples in 1896. The particular case has become popularized as the one-seventh area triangle. The case implies that the three medians are concurrent (through the centroid). (Wikipedia).
