Euclidean Parallelism
Given straight lines l and m, the following descriptions of line m equivalently define it as parallel to line l in Euclidean space:
- Every point on line m is located at exactly the same minimum distance from line l (equidistant lines).
- Line m is on the same plane as line l but does not intersect l (even assuming that lines extend to infinity in either direction).
- Lines m and l are both intersected by a third straight line (a transversal) in the same plane, and the corresponding angles of intersection with the transversal are congruent. (This is equivalent to Euclid's parallel postulate.)
In other words, parallel lines must be located in the same plane, and parallel planes must be located in the same three-dimensional space. A parallel combination of a line and a plane may be located in the same three-dimensional space. Lines parallel to each other have the same gradient. Compare to perpendicular.
Read more about this topic: Parallel (geometry)
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