Two lines in two-dimensional Euclidean space are said to be parallel if they do not intersect. In
three-dimensional Euclidean space, parallel
lines not only fail to intersect, but also maintain
a constant separation between points closest to each other on the two lines. Lines
in three-space that are not parallel but do not intersect
are called skew lines.
If lines
and are parallel, the notation is used.
In a non-Euclidean geometry, the concept of parallelism must be modified from its intuitive meaning. This is accomplished
by changing the so-called parallel postulate.
While this has counterintuitive results, the geometries so defined are still completely
self-consistent.
In a triangle, a triangle median bisects all segments parallel to
a given side
(Honsberger 1995, p. 87).
and 
are parallel, the notation 
is used.
, a triangle median 
bisects all segments parallel to
a given side 
(Honsberger 1995, p. 87).
