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 …

Menelaus' Theorem deals with the collinearity of points on each of the three sides (extended when necessary) of a triangle. It is named after Menelaus of Alexandria.

Menelaus' theorem relates ratios obtained by a line cutting the sides of a triangle. The converse of the theorem (i.e. three points on a triangle are collinear if and only if they satisfy certain criteria) is also …

Dec 3, 2025 · "The Theorem of Menelaus." Ch. 13 in Episodes in Nineteenth and Twentieth Century Euclidean Geometry. Washington, DC: Math. Assoc. Amer., pp. 147-154, 1995. Pedoe, D. Circles: A …

Jun 17, 2024 · Theorem Let $ABC$ be a triangle. Let points $D, E, F$ lie on lines $BC, AC, AB$ respectively (produced if necessary). Then $D, E$ and $F$ are collinear if and only if: $\dfrac {AF} …

May 16, 2025 · Menelaus' Theorem, sometimes known as Menelaus' Lemma, is a classical result in Euclidean geometry that provides necessary and sufficient conditions for three points lying on the …

Theorem 1.2 (Menelaus's Theorem, Basic Version). Choose X on the line BC but not on the segment BC, choose Y on the (interior of the) line segment AC, and Z on the (interior of the) line segment AB.

Menelaus’ theorem shows a pattern that is observed for the relationships of segments that connect the vertices of a triangle and the points of intersection of the secant with the sides (extensions of the …

Oct 13, 2009 · Like Ceva’s theorem, Menelaus' theorem shows that a geometrical condition, collinearity, is equivalent to an arithmetical condition for ratios. The two theorems are very similar, and in a …

Aug 19, 2014 · A theorem on the relations between the lengths of the segments on the sides of a triangle determined by an intersecting straight line. It asserts that if the given line intersects the sides …