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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 at Hanoi, Hanoi, 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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