Morley's trisector theorem

For any triangle, the three pairwise intersections of adjacent internal angle trisectors form an equilateral triangle.

Angle trisection: Angle trisection divides an angle into three equal angles. Each vertex angle is divided into thirds before adjacent trisectors intersect.
Triangle: A polygon with three sides and three interior angles. The theorem applies to every triangle, regardless of its side lengths or angle sizes.
Frank Morley: An American mathematician known for work in geometry and for the theorem bearing his name. His name became attached to the trisector result, although its discovery predates its publication.
Equilateral triangle angle trisectors: The internal trisectors drawn from the vertices of an equilateral triangle. Symmetry makes the resulting Morley triangle especially easy to locate and verify.
Angle bisector theorem: A theorem relating the lengths into which an angle bisector divides the opposite side of a triangle. It concerns bisector intersections with sides, not intersections among trisectors.
Equilateral triangle: A triangle with three equal sides and three equal angles of 60 degrees. The three trisector intersections have pairwise equal angles and form this triangle.
Internal angle bisector: A ray from a triangle vertex that divides its interior angle into two equal angles. Trisectors are defined by subdividing the same interior angles that bisectors divide in half.
Morley's trisector theorem proof history: The history of the theorem's discovery, publication, and early proofs. The result circulated before a proof appeared in print.
Isosceles triangle: A triangle with at least two equal sides. Its reflection symmetry makes two of the three trisector intersections correspond.
Exterior angle trisectors: Lines that divide a triangle's exterior angles into three equal parts. The stated equilateral-triangle result uses internal trisectors, not this different configuration.

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