||This article may be too technical for most readers to understand. (November 2012)|
In geometry, anti-parallel lines can be defined with respect to either lines or angles.
Given two lines and , lines and are anti-parallel with respect to and if . If and are anti-parallel with respect to and , then and are also anti-parallel with respect to and .
In any quadrilateral inscribed in a circle, any two opposite sides are anti-parallel with respect to the other two sides.
Two lines and are said to be antiparallel with respect to the sides of an angle if they make the same angle in the opposite senses with the bisector of that angle.
In a vector space over (or some other ordered field), two nonzero vectors are called antiparallel if they are parallel but have opposite directions. In that case, one is a negative scalar times the other.
- The line joining the feet to two altitudes of a triangle is antiparallel to the third side.(any cevians which 'see' the third side with the same angle create antiparallel lines)
- The tangent to a triangle's circumcircle at a vertex is antiparallel to the opposite side.
- The radius of the circumcircle at a vertex is perpendicular to all lines antiparallel to the opposite sides.