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Not parallel to itself
- 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.
brilliant.org/wiki/parallel-lines/
Aug 11, 2011 · 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). $\endgroup$
- In classical geometry why is a line considered to be parallel ...
In the first case they are said to intersect in their common...
- geometry - Is a line, that's contained in a plane, parallel ...
In 2 dimensional Geometry, I have never heard of the...
- In classical geometry why is a line considered to be parallel ...
Apr 18, 2018 · 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 $l$ is always regarded as parallel to itself.
Mar 12, 2021 · In 2 dimensional Geometry, I have never heard of the specification that a line is parallel to itself. This (inconclusively) suggests that in 3 dimensional Geometry, a line can not be considered parallel to the plane that contains the line.
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.
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.
Conditions for Lines to be parallel. If two straight lines are cut by a transversal, the pair of alternate angles are equal, then two straight lines are parallel to each other. the pair of interior angles on the same side of traversals is supplementary, then the two straight lines are parallel.
Two lines are parallel lines if they do not intersect at any point or if they coincide. The symbols // or || are used to indicate two parallel lines. r//s r / / s r ∥ s r ∥ s. The region between the two lines is called a " strip " or " band."
