Menelaus's theorem
In Euclidean geometry, Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle △ABC, and a transversal line that crosses BC, AC, AB at points D, E, F respectively, with D, E, F distinct from A, B, C. A weak version of the theorem states that | A F ¯ F B ¯ | × | B D ¯ D C ¯ | × | C E ¯ E A ¯ | = 1 , {\displaystyle \left|{\frac {\overline {AF}}{\overline {FB}}}\right|\times \left|{\frac {\overline {BD}}{\overline {DC}}}\right|\times \left|{\frac {\overline {CE}}{\overline {EA}}}\right|=1,} where "| |" denotes absolute value (i.e., all segment lengths are positive).