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).
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.
Kern, W. F. and Bland, J. R. Solid Mensuration with Proofs, 2nd ed. New York: Wiley,
p. 9, 1948.
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