A New Geometric Proof for Morley’s Theorem

Abstract

This article gives a new and purely geometric proof for Morley’s theorem. Morley’s theorem is one of the most elegant results of elementary geometry, and can be stated as follows. The three points of intersection of the adjacent trisectors of the angles of any triangle form an equilateral triangle (Figure 1). The theorem admits a wide variety of proofs. An excellent review covering the proofs prior to 1978 can be found in [3]. A recent review can be found in [2, Section 10]. Finally, the recent proofs alongside the most popular ones can be traced through the web article [1]. Yet another new and purely geometric proof is given in this article.