Morley's trisector theorem

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In plane geometry, Morley's trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the Morley triangle. The theorem was discovered in 1899 by Anglo-American mathematician Frank Morley. It has various generalizations, in particular if all of the trisectors are intersected one obtains four other equilateral triangles.

There are several proofs to Morley's theorem, many of which are in depth. Most of these proofs begin with an equilateral triangle and prove that a triangle may be built around it which, when scaled, will be congruent to a selected triangle. More direct proofs are also available.

[edit] External links

• Morley's theorem - Introduction with animation by Antonio Gutierrez from Geometry Step by Step from the Land of the Incas.
• Morley's Miracle — Several proofs of Morley's theorem at cut-the-knot
• Modern Mathematical Milestones: Morley's Mystery by Richard L. Francis (pdf)