Antiparallel

Two lines $PQ$ and $RS$ 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 $PQ$ and $RS$ are antiparallel with respect to $PR$ and $QS$, then the latter are also antiparallel with respect to the former. Furthermore, if $PQ$ and $RS$ are antiparallel, then the points $P$, $Q$, $R$, and $S$ are Concyclic (Johnson 1929, p. 172; Honsberger 1995, pp. 87-88).

See also Hyperparallel, Parallel

References

Honsberger, R. ``Parallels and Antiparallels.'' §9.1 in Episodes in Nineteenth and Twentieth Century Euclidean Geometry. Washington, DC: Math. Assoc. Amer., pp. 87-88, 1995.

Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, p. 172, 1929.