In reality they would never meet. But mathematically speaking, they would meet at infinity. Infinity is only a relative term.
In Euclidean geometry, they do not meet.
Parallel lines by definition never cross each other.
It is an axiom that parallel lines never meet in Euclidean geometry. Never.However in another kind of geometry (can't remember name) it states that parallel lines will eventually meet.Take a look at this picture in the related link, below.Technically the lines are parallel (in theory, they have imperfections), but due to our perspective parallel lines appear to meet. Note: If they really do meet, then you could drive down the road and eventually there would not be a road, anymore.
In Euclidian geometry, which is the geometry of a plane surface, parallel lines do not intersect because that is the definition of parallel lines. But note that there are other geometrical systems in which parallel lines do intersect, for example if they are drawn on the surface of a sphere. Definition of parallel lines: Lines that always stay the same distance apart and never meet.
Yes, in plane geometry parallel lines continue forever. However, in polar geometry (3 dimensions, as in Earth longitudinal lines), parallel lines eventually intersect at the poles of the sphere,
In Euclidean geometry, they do not meet.
In plane geometry, the geometry of a flat surface, parallel lines by definition never meet. However in spherical geometry, the geometry of the surface of a sphere (such as the planet Earth) parallel lines meet at the poles.
Parallel lines by definition never cross each other.
By definition, perpendicular lines are those which meet in a right angle. So, yes, they have to meet in order to be "perpendicular". Parallel lines may, or may not, meet, depending on how you choose your axioms. In Euclidean geometry, parallel lines never meet. In certain types of non-Euclidean geometry, they can meet.
In Euclidean geometry, parallel lines are the same distance apart and never meet.
It is an axiom that parallel lines never meet in Euclidean geometry. Never.However in another kind of geometry (can't remember name) it states that parallel lines will eventually meet.Take a look at this picture in the related link, below.Technically the lines are parallel (in theory, they have imperfections), but due to our perspective parallel lines appear to meet. Note: If they really do meet, then you could drive down the road and eventually there would not be a road, anymore.
No, in Euclidean geometry they do not meet.
In Euclidian geometry, which is the geometry of a plane surface, parallel lines do not intersect because that is the definition of parallel lines. But note that there are other geometrical systems in which parallel lines do intersect, for example if they are drawn on the surface of a sphere. Definition of parallel lines: Lines that always stay the same distance apart and never meet.
An angle has lines that meet at the angle end, but that stretch apart at the other end. Parallel lines are like railway lines. They go on and on and never meet.
Yes. You can use this to prove that two lines are parallel, in analytic geometry, i.e., geometry that uses coordinates.Yes. You can use this to prove that two lines are parallel, in analytic geometry, i.e., geometry that uses coordinates.Yes. You can use this to prove that two lines are parallel, in analytic geometry, i.e., geometry that uses coordinates.Yes. You can use this to prove that two lines are parallel, in analytic geometry, i.e., geometry that uses coordinates.
Lines that meet are not parallel, and parallel lines never meet.
On a flat surface, in plane geometry, two parallel lines never meet; they are perfectly aligned with each other, so that they neither approach nor diverge from each other, at any distance. Parallel lines can meet at the poles, but not in plane geometry; this happens in spherical geometry. If the lines are on a sphere, such as, for example, the lines of longitude that are used (in conjunction with lines of latitude) to specify locations on the planet Earth, parallel lines meet at the poles. On a large scale, these parallel lines look completely different from those of plane geometry, but on a small scale, these huge circles will look much like line segments of plane geometry. Over short distances, the spherical surface of the Earth appears to be flat.