Two lines P Q and R S are said to be antiparallel with respect to the sides of an angle A if they make the same angle in the opposite senses with the bisector of that angle. If P Q and R S are antiparallel with respect to P R and Q S, then the latter are also antiparallel with respect to the former. Furthermore, if P Q and R S are antiparallel, then the points P, Q, R, and S are concyclic (Johnson 1929, p. 172; Honsberger 1995, pp. 87-88). There are a number of fundamental relationships involving a triangle and antiparallel lines. 1. The line joining the feet to two altitudes of a triangle is antiparallel to the third side.

angle | concyclic | cosine circle | cosine hexagon | first Lemoine circle | hyperparallel | Lemoine hexagon | parallel | Tucker circles | Tucker hexagon