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The idea or concept of parallel lines is defined by Euclidean geometry as lines that never cross. So the regular answer is: No, they never cross, because then they will not be parallel according to Euclid.
But, I'm sure the questioner is not asking about Euclidean geometry but about reality.
In this sense some people will say: No, parallel never cross because there is no such a thing in real life. Parallel lines only exist in our mind.
But this answer is too simplistic. There is "reality" in our "ideal" concept of parallel lines. If reality was so disconnected from our geometric and logical constructs we would not be able to interact with the real world. We can walk, see and reason reality because we find circles, lines, logical constructs and 2 as the sum of 1 + 1, in the "real" world. Or at least, a very close approximation to that, though never "perfect" circles or lines.
Kant clearly demonstrated that these ideas are "hard coded" in our mind, not learned, because we need this idea "framework" to rationalize perception in the first place. There has never been a society where 1+1=3 and where parallel lines cross at say, 100 feet.
Questions like these are the beginning of modern philosophy, beginning with Plato who had not other option but to conclude that these ideas have an existence of their own in some kind of idea heaven. Of course the point is not whether this idea heaven exists, but to point out the real problems: Why do we have this constructs in our mind? What is the relationship to reality? Where do ideas come from?
So, in summary, yes, parallel lines in our mind never cross, and yes, they seem not to exist in reality. But there is a very real connection between the idea and the "real" thing, but since we can only "see" the "idea" we can not now in "reality".
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∙ 12y ago
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What lines that are not parallel never cross?
Diverging lines are not parallel and never cross.
Lines that never cross?
Parallel lines
Two lines that never cross?
Parallel lines never intersect/cross.
What are coplanar lines that don't cross?
Parallel lines
What are two lines called that never cross each other?
parallel lines
Can parallel lines ever cross each other?
No, parallel actually means that the lines will never touch or cross
What does the word parallel mean in maths?
Parallel in maths means opposite. Two parallel lines can never touch. I you are not sure if two lines are parallel then imagine that these lines go on for ever, will they eventually cross?
What lines that are not parallel never cross?
Diverging lines are not parallel and never cross.
What is Perpendicular and Parallel?
Perpendicular is when two lines cross... Parallel is when two lines never meet.... _____________ _____________ = PARALLEL LINES If they cross they are perpendicular, if they don't, they are parallel.
What are lines that never crossed called?
Parallel lines are lines that never cross.
Lines that never cross?
Parallel lines
What are Lines that do not cross?
Parallel
Two lines that never cross?
Parallel lines never intersect/cross.
What are coplanar lines that don't cross?
Parallel lines
What are the deference between parallel lines and intersecting lines?
The difference between intersecting and parallel lines is that, on a graph parallel lines do ont touch,cross or anything. THEY NEVER TOUCH. intersecting lines touch, or cross eachother.\
Two lines are perpendicular if they are parallel and cross?
Parallel lines are never perpendicular. Perpendicular lines are co-planar and cross at right angles.
What are two lines called that never cross each other?
parallel lines
