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- According to the axioms of Euclidean geometry, a line is not parallel to itself, since it intersects itself infinitely often. However, some authors allow a line to be parallel to itself, so that "is parallel to" forms an equivalence relation.
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Aug 11, 2011 · Howether it depends from your definition. Following Wikipedia en.wikipedia.org/wiki/Parallel_%28geometry%29, the answer is yes according to definition 1 (each point of a line has distance zero from the line), and it is no according to definition 2 (a line clearly intersect itself). – Giovanni De Gaetano.
Apr 18, 2018 · In consequence of Postulate II, any two distinct lines l, m l, m have either one point in common or none. In the first case they are said to intersect in their common point; in the second case, they are said to be parallel; a line l l is always regarded as parallel to itself. Share.
Mar 12, 2021 · A line is parallel to plane if the normal of the plane is perpendicular to the line. Definition from Wikipedia seems to say no; from the first definition "parallel lines are lines in a plane which do not meet", and the plane and line has to "keep a fixed minimum distance".
In the first case they are intersecting (briefly \(\ell \nparallel m\)); in the second case, l and m are said to be parallel (briefly, \(\ell \parallel m\)); in addition, a line is always regarded as parallel to itself. To emphasize that two lines on a diagram are parallel we will mark them with arrows of the same type.
Properties of Parallel Lines. Before talking about lines that are parallel to the same line, let us recall what parallel lines are. Non-intersecting or parallel lines are the lines that do not intersect each other. They are always at the same distance from one another.
According to the axioms of Euclidean geometry, a line is not parallel to itself, since it intersects itself infinitely often. However, some authors allow a line to be parallel to itself, so that "is parallel to" forms an equivalence relation.
Jun 4, 2024 · Parallel lines are always equidistant from each other, they lie on the same plane and they meet at infinity. Learn, definitions, pair of angles, properties, symbol, examples, and FAQs on parallel lines in detail.
