Question

comparing euclidean and non - euclidean geometries
which statement represents the parallel postulate in euclidean geometry, but not elliptical or spherical geometry?
through a given point not on a line, there exists no lines parallel to the given line through the given point.
through a given point not on a line, there exists exactly one line parallel to the given line through the given point.
through a given point not on a line, there exists more than one line parallel to the given line through the given point.
through a given point not on a line, there exists exactly three lines parallel to the given line through the given point.

Explanation:

In Euclidean geometry, the parallel postulate states that through a given point not on a line, there exists exactly one line parallel to the given line. In elliptical or spherical geometry, there are no parallel lines (any two lines intersect), so this postulate only holds in Euclidean geometry.

Answer:

Through a given point not on a line, there exists exactly one line parallel to the given line through the given point.