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Elliptical geometry is a non-Euclidean geometry. The parallel postulate of Euclidean geometry was replaced by the statement that through any point in the plane, there exist no lines parallel to a given line. A consistent geometry - of a space with positive curvature - was developed on that basis.
It is, therefore, by definition that parallel lines do not exist in elliptical geometry.
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∙ 8y ago
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∙ 8y agobecause all great circles intersect
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Two parallel lines have equal slope?
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.
Are two lines that lie in parallel planes always sometimes or never parallel?
SOMETIMES. I just did that problem in my California geometry book. They can either be parallel or skew...making the answer sometimes.
How many parallel lines does a cone have?
A cone does not have any parallel lines
What are some examples of parallel lines and a pair of perpendicular lines?
Railroad tracks or the number 11 are parallel lines. A cross or a small t are perpendicular lines. Also the two ll's in the middle of parallel are parallel lines.
What is parallel line segment?
lines which lie in same pane are known as parallel lines or lines which do not intersect are known as parallel lines they extend in both the direction
Two parallel lines have equal slope?
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.
Do parallel lines run from the north to south pole?
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.
What is ll in geometry?
Parallel lines
What is the difference between Euclidean Geometry and non-Euclidean Geometry?
In Euclidean geometry parallel lines are always the same distance apart. In non-Euclidean geometry parallel lines are not what we think of a parallel. They curve away from or toward each other. Said another way, in Euclidean geometry parallel lines can never cross. In non-Euclidean geometry they can.
Do all parallel lines intersect?
No. In ordinary Euclidean geometry, parallel lines neverintersect.
Do parallel lines continue forever?
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,
What geometry has parallel lines meet?
Parallel lines by definition never cross each other.
Parallel lines are equidistant and will never meet?
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.
How many points do tree parallel lines intersect?
None. Parallel lines do not intersect in Euclidean geometry.
Why can't parallel lines intersect?
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.
Are parallel lines coplanar?
In Euclidean geometry, parallel line are alwayscoplanar.
Is parallel lines meet?
In Euclidean geometry, they do not meet.
