On some extensions of Morley's trisector theorem
Nikos Dergiades, Tran Quang Hung

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.
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Taxonomy
TopicsMathematics and Applications · History and Theory of Mathematics · graph theory and CDMA systems
