The first Morley triangle 
, also simply known as "Morley's triangle",
is the triangle constructed from pairwise intersections of the angle
trisectors of a given triangle 
. In particular, its 
-vertex is the point of intersection of the first trisector
of 
when swinging 
counterclockwise about 
and the first trisector of 
, with the 
- and 
-vertices similarly defined (Kimberling 1998, p. 165).
By Morley's theorem, this triangle is equilateral.
It has trilinear vertex matrix
![[1 2cos(1/3C) 2cos(1/3B); 2cos(1/3C) 1 2cos(1/3A); 2cos(1/3B) 2cos(1/3A) 1]](/images/equations/FirstMorleyTriangle/NumberedEquation1.svg) |
(Kimberling 1998, p. 165).
It has side lengths
 |
where 
is the circumradius of the original triangle.
All triangle centers of the first Morley triangle concur at the first Morley center of the reference triangle.
The following table lists perspectors of the second Morley triangles with other named triangles that are Kimberling centers.
| excentral triangle |  | first Morley-Gibert point |
| first Morley adjunct triangle |  | first Morley center |
| reference triangle |  | first Morley-Taylor-Marr center |
| second Morley triangle |  | second Morley-Taylor-Marr center |
| third Morley triangle |  | 4th Morley-Taylor-Marr center |
