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A Short Proof of Morley's Trisector Theorem

Brian R Stonebridge, A Short Proof of Morley's Trisector Theorem. CSTR-95-018, Department of Computer Science, University of Bristol. August 1995. No electronic version available.

Abstract

Anyone who has tackled the proof of Morley's theorem will almost certainly have encountered a situation of having two sets of angles - one set easy to determine, the other not obvious. This report destroys the pleasure and the education to be derived from seeking a solution. Morley's theorem states that the points of intersection of the adjacent trisectors of any triangle form an equilateral triangle. We give a new, short proof, which uses a direct forward approach. It makes use of symmetry to make a dramatic reduction in the length of proof. Other known proofs are longer and usually work backwards or are restricted to acute-angled triangles. Most do not capture the problem's essential symmetric and geometric properties.

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