Question

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.

Answer 1

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

Answer 2

Option B is the right answer.

Explanation:

Which statement represents the parallel postulate in Euclidean geometry, but not elliptical or spherical geometry?

The correct statement is - Through a given point not on a line, there exists exactly one line parallel to the given line through the given point.

The parallel postulate in Euclidean geometry states that through any given point not on a line there passes exactly one line parallel to that line in the same plane.