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 …

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 …

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.

Jul 5, 2022 · Theorem (Menelaus’ Theorem) Three points, one non-vertex point from each side line of a triangle, are collinear if and only if the product of the signed ratios they determine on …

In their most basic form, Ceva’s Theorem and Menelaus’s Theorem are simple formulas of triangle geometry. To state them, we require some de nitions. Three or more line segments in …

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 …

Menelaus' theorem states that if X, Y and Z are collinear, then equality (1) holds. Does the converse of Menelaus' theorem also hold? That is, if X, Y and Z are points such that equality …

Apr 30, 2025 · is the ratio of the lengths and with a plus or minus sign depending if these segments have the same or opposite directions (Grünbaum and Shepard 1995). The case is …

The condition of Menelaus’ theorem can be generalized to cross ratios (see fileCross ratio ) by introducing an arbitrary line ε , which together with the other four lines forms a set in general …

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 …