Are coinciding lines parallel?

Question

I have a question about parallel lines and coincident lines. According to wikipedia a parallel line is:

Two lines in a plane that do not intersect or touch at a point are called parallel lines.

But another reference says

Side by side and having the same distance continuously between them.

And two coincident lines follow each of the given two conditions i.e. they do not intersect at a point (as they intersect in more than one point) and also the distance between them remians same. So are two coinciding lines parallel or am I missing something.

See also the post : In classical geometry why is a line considered to be parallel to itself ? — Mauro ALLEGRANZA, Jun 25 '18 at 15:19
The level of duplication in this question to a previous one is remarkable. It's hard to believe that this is coincidental. If you saw that question and were not satisfied with the answers, you could/should revise your own question to reference the other one, and ask for responses that address specific points you need clarified. — Blue, Jun 25 '18 at 15:21
@TheMathemagician Please recall that if the OP is solved you can evaluate to accept an answer among the given, more details here https://meta.stackexchange.com/questions/5234/how-does-accepting-an-answer-work — user, Aug 05 '18 at 20:57

score 0 · Answer 1 · answered Jun 25 '18 at 15:18

Yes of course, as trivial case, two coinciding lines are parallel in the sense that, with reference to the parametric equation, their direction vectors $v$ and $w$ are parallel

$L_1: P_1+t\,v$
$L_2: P_2+t\, w$

with $v\parallel w$ and $P_1\in L_2$.

Are coinciding lines parallel?

1 Answers1