Parallel (geometry)
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Parallel is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. The existence and properties of parallel lines are the basis of Euclid's parallel postulate.
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Parallel_lines.png
Parallel_lines.png
As shown by the tick marks, lines a and b are parallel. We can prove this because the transversal t produces congruent angles.
- When lines or planes are parallel, then every point on one is located exactly the same minimum distance from the other line or plane.
- Another way of defining it is that any two parallel lines or planes, if extended to infinity in both directions, will never intersect. This second definition carries the condition that the extension must occur only in one additional dimension: 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.
- A third definition is: if two lines are both intersected by a third line (a transversal) in the same plane, and the angles of intersection are equal, then the two lines are parallel.
Lines parallel to each other have the same gradient.
Compare to perpendicular.da:Parallel de:Parallele (Geometrie) eo:Paralelo ja:平行 nl:Parallellie zh:平行 (几何学)