# Can there be parallel lines on a sphere?

## Can there be parallel lines on a sphere?

If there is a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line. There are no parallel lines in spherical geometry.

## How many pairs of parallel lines are there in a sphere?

In spherical geometry, because there are no parallel lines, these two perpendiculars must intersect. But there is something more subtle involved in this third postulate. All perpendiculars meet at the same point.

Can great circles ever be parallel?

There are no non-intersecting great circles. Any two great circles intersect in two opposite points. So there are no parallel “lines” (great circles) on a sphere.

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Why are there no parallel lines on sphere?

In spherical geometry Parallel lines DO NOT EXIST. In Euclidean geometry a postulate exists stating that through a point, there exists only 1 parallel to a given line. Therefore, Parallel lines do not exist since any great circle (line) through a point must intersect our original great circle.

### How many lines are on a sphere?

We all know that the shortest path between two points on a plane is a straight line. On the surface of a sphere, however, there are no straight lines.

### What happens to parallel lines on a sphere?

What are the five main parallel lines?

The five major parallels of latitudes from north to south are called: Arctic Circle, Tropic of Cancer, Equator, Tropic of Capricorn, and the Antarctic Circle.

Do parallel lines exist?

#### In which geometry are there no parallel lines?

In spherical geometry, straight lines are great circles, so any two lines meet in two points. There are also no parallel lines. The angle between two lines in spherical geometry is the angle between the planes of the corresponding great circles, and a spherical triangle is defined by its three angles.