Medial Triangle - Anticomplementary Triangle

If XYZ is the medial triangle of ABC, then ABC is the anticomplementary triangle or antimedial triangle of XYZ. The anticomplementary triangle of ABC is formed by three lines parallel to the sides of ABC: the parallel to AB through C, the parallel to AC through B, and the parallel to BC through A.

Trilinear coordinates for the vertices of the anticomplementary triangle, X'Y'Z', are given by

• X' = −1/a : 1/b : 1/c
• Y' = 1/a : −1/b : 1/c
• Z' = 1/a : 1/b : −1/c

The name "anticomplementary triangle" corresponds to the fact that its vertices are the anticomplements of the vertices A, B, C of the reference triangle. The vertices of the medial triangle are the complements of A, B, C.