In this case, no additional condition is necessary because they always belong to the "same space". Analoguously, in three-dimensional space two planes, or a line and a plane, are said to be parallel if they do not intersect.(Transitivity) If among three distinct lines two pairs of lines are parallel then the third pair is also parallel.(This means, more precisely, that all distances from a point on one of them to the other line are the same.) (Equidistant lines) Parallel lines have constant distance.(Uniqueness) Given a line then through any point (not on it) there is a uniquely determined line parallel to the given one.Important properties of the notion "parallel" in Euclidean geometry are: Non-intersecting lines that do not belong to a common plane are called skew. In it, the explicit condition "in a plane" is necessary because in space two straight lines that do not intersect need not be parallel. This definition is correct if (silently) the "natural" ( Euclidean) geometry is assumed.
The term parallel is also used for line segments that are part of parallel lines. Parallel (or parallel to each other) if they do not meet (or intersect), i.e., do not have a point in common. Straight railway tracks may be considered as segments of parallel lines, railway tracks with curves are parallel curves.Īccording to the common explanation two straight lines in a plane are said to be
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