In geometry, **anti-parallel lines** can be defined with respect to either lines or angles.

Given two lines
m
1
and
m
2
, lines
l
1
and
l
2
are anti-parallel with respect to
m
1
and
m
2
if
∠
1
=
∠
2
in Fig.1. If
l
1
and
l
2
are anti-parallel with respect to
m
1
and
m
2
, then
m
1
and
m
2
are also anti-parallel with respect to
l
1
and
l
2
.

In any quadrilateral inscribed in a circle, any two opposite sides are anti-parallel with respect to the other two sides (Fig.2).

Two lines
l
1
and
l
2
are antiparallel with respect to the sides of an angle if and only if they make the same angle
∠
A
P
C
in the opposite senses with the bisector of that angle (Fig.3).

In a Euclidean space, two directed line segments, often called *vectors* in applied mathematics, are **antiparallel**, if they are supported by parallel lines and have opposite directions. In that case, one of the associated Euclidean vectors is the product of the other by a negative number.

- 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.