On some extensions of Morley's trisector theorem

TL;DR

This paper presents new extensions of Morley's trisector theorem, providing simple synthetic proofs for these generalizations and their converses, expanding the understanding of triangle trisectors.

Contribution

It introduces novel extensions of Morley's theorem with straightforward synthetic proofs and explores their converses, enhancing geometric theorem generalizations.

Findings

New extensions of Morley's theorem established

Synthetic proofs based solely on angle chasing and similarity

Additional simple extensions derived from converse constructions

Abstract

We establish a simple generalization for the famous theorem of Morley about trisectors in triangle with a purely synthetic proof using only angle chasing and similar triangles. Furthermore, based on the converse construction, another simple extension of Morley's Theorem is created and proven.