The first Morley adjunct triangle is the triangle Δ A'' B'' C'' illustrated above, where Δ A' B' C' is the first Morley triangle. Unlike the first Morley triangle, the first Morley adjunct triangle is not equilateral. The first Morley adjunct triangle has trilinear vertex matrix [2 | sec(1/3 C) | sec(1/3 B) sec(1/3 C) | 2 | sec(1/3 A) sec(1/3 B) | sec(1/3 A) | 2] (Kimberling 1998, p. 167).

first Morley triangle | second Morley adjunct triangle | third Morley adjunct triangle