Orthologic triangles

In geometry, two triangles are said to be orthologic if the perpendiculars from the vertices of one of them to the corresponding sides of the other are concurrent (i.e., they intersect at a single point).

This is a symmetric property; that is, if the perpendiculars from the vertices A, B, C of triangle △ABC to the sides EF, FD, DE of triangle △DEF are concurrent then the perpendiculars from the vertices D, E, F of △DEF to the sides BC, CA, AB of △ABC are also concurrent.

The points of concurrence are known as the orthology centres of the two triangles.

[1][2] The following are some triangles associated with the reference triangle ABC and orthologic with it.

[3]