Reformulasi dan Pembuktian Teorema Menelaus menggunakan Variabel Kompleks

Abstract

This study aims to reformulate and prove Menelaus’s Theorem using a complex variable approach. In classical Euclidean geometry, Menelaus’s Theorem states that three points, each lying on a side or the extension of a side of a triangle, are collinear if and only if the product of the ratios of the lengths of the resulting line segments equals one. Through a complex algebraic approach, this study systematically reorganizes the proof of the theorem and represents the geometric structure of triangles and straight lines in the complex plane. The representation of points and line segments, along with the use of fundamental properties such as conjugates and modulus, is employed to prove the theorem analytically. The findings of this study confirm that the use of complex variables provides an efficient analytical framework for deriving geometric proofs, resulting in a more systematic logical flow compared to the classical geometric approach. This study offers a new perspective on the development of modern geometry and opens up opportunities for further exploration in the application of complex variables to solve other geometric problems.