| 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 Line s or Planes , or a combination of these. The existence and properties of '''parallel lines''' are the basis of Euclid 's Parallel Postulate . EUCLIDEAN PARALLELISM ''t'' produces congruent angles.]] =( 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 exactly the same minimum distance from line ''l'' ('equidistant lines', not including the degenerate case where ''m = l''). #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 equal. 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 . Construction The three definitions above lead to three different methods of construction of parallel lines. |
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