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I understand your question to be, "Is it true that parallel lines are everywhere equidistant and never intersect?"
In what follows, I assume we're talking about a two-dimensional plane.
By definition, two lines that are parallel (in the same plane) never intersect. In Euclidean (AKA Parabolic or simply E) Geometry, and also in Hyperbolic (AKA simply L) Geometry, parallel lines exist. In Elliptical (AKA R) Geometry, all lines eventually intersect so parallel lines do not exist.
Now, are two parallel lines (in the same plane) everywhere equidistant? If so, that means that it is possible, at any point on one of the lines, to construct a perpendicular that will meet the other line in a perpendicular, and that the length of the segments constructed will be always the same.
In Euclidean Geometry, two parallel lines (in a plane) are indeed everywhere equidistant. To prove it requires the converse of the Alternate Interior Angles theorem (AIA), which says that if two parallel lines are cut by a transversal, the alternate interior angles will be congruent. Note that this is the CONVERSE of AIA, not AIA. Some people get this mixed up.
In Hyperbolic Geometry, two lines can be parallel, but be further apart some places than others. I know that sounds rather odd, if you're not used to it. Here's an image that might help: imagine that your plane is a thin sheet of rubber, and for some reason is being stretched. The further you go from your starting point, the more it stretches, and it's always stretching away from you. This means that your parallel lines will keep getting further and further apart.
What else can I help you with?
What do you call lines in a plain that do not meet?
Parallel lines are equidistant apart and never meet
What type of lines (falling in the same plane) are equidistant apart and never meet?
They are parallel lines
What do you call a paralla lines that meet?
Parallel lines, by definition, never meet or intersect, as they are always equidistant from each other. If lines do meet, they are not parallel. If two lines that are not parallel intersect at a single point, they are referred to as intersecting lines.
What are 2 lines that never meet?
Two lines that never meet are called parallel lines. They remain equidistant from each other at all points and do not intersect, regardless of how far they are extended. An example of parallel lines can be seen in the rails of a train track.
Which lines does not meet together?
The lines that do not meet together are called non-intersecting or parallel lines. These lines remain equidistant from each other and never cross at any point, regardless of how far they are extended. In a two-dimensional space, only straight lines can be classified as parallel.
What do you call lines in a plain that do not meet?
Parallel lines are equidistant apart and never meet
What type of lines (falling in the same plane) are equidistant apart and never meet?
They are parallel lines
What do you call a paralla lines that meet?
Parallel lines, by definition, never meet or intersect, as they are always equidistant from each other. If lines do meet, they are not parallel. If two lines that are not parallel intersect at a single point, they are referred to as intersecting lines.
What are 2 lines that never meet?
Two lines that never meet are called parallel lines. They remain equidistant from each other at all points and do not intersect, regardless of how far they are extended. An example of parallel lines can be seen in the rails of a train track.
Which lines does not meet together?
The lines that do not meet together are called non-intersecting or parallel lines. These lines remain equidistant from each other and never cross at any point, regardless of how far they are extended. In a two-dimensional space, only straight lines can be classified as parallel.
Do parallel lines meet at a 30 dregrese angle?
Lines that meet are not parallel, and parallel lines never meet.
Two lines that never meet?
Parallel Lines will never meet
Do intersecting lines never meet?
No but parallel lines never meet
Why do parallel lines meet in the distance?
parallel lines never meet. it is an optical illusion
Which lines will never meet?
Parallel lines
Do parallel lines ever meet?
Parallel lines never ever meet with each other
What are lines that never meet called?
parallel lines
