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Journal for Geometry and Graphics 24 (2020), No. 2, 197--205
Copyright Heldermann Verlag 2020

On some Extensions of Morley’s Trisector Theorem

Nikos Dergiades
Thessaloniki, Greece

Tran Quang Hung
High School for Gifted Students, Vietnam National University, Vietnam

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

Keywords: Morley's trisector theorem, Morley's triangle, equilateral triangle, perspective triangle.

MSC: 51M04; 51-03

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