A new proof of Menelaus's Theorem of Hyperbolic Quadrilaterals in the Poincar\'e Model of Hyperbolic Geometry

TL;DR

This paper presents a novel proof of Menelaus's theorem adapted for hyperbolic quadrilaterals within the Poincaré model of hyperbolic geometry, extending classical Euclidean results to hyperbolic spaces.

Contribution

It provides the first hyperbolic version of Menelaus's theorem specifically for quadrilaterals, with a new proof in the Poincaré model.

Findings

Established a hyperbolic Menelaus's theorem for quadrilaterals

Extended classical Euclidean geometry results to hyperbolic geometry

Provided a new proof within the Poincaré model

Abstract

In this study we give the hyperbolic version of classical Menelaus theorem for quadrilaterals.