parallel postulate- help asap please!?

Question

on a plane, there is a line and a point not on the line. how many lines can be drawn through it that are parallel to the first line?

what about on a sphere?

and how do alternate angles and corresponding angles hold for spherical geometry?

Answer 1

on a plane, given point and line, only 1 parallel (in euclidean geometry).

on a sphere, where "line" means great circle, the intersection of the sphere with a plane that contains the center of the sphere, there are no parallel lines.

without parallels, no sense talking about alternate or corresponding angles.

Answer 2

Not enough info.

Are the line and point on the same plane? If so, then I wouldn't discuss the sphere. Planes can be parallel in 3 dimensions, but lines? In 3 dimensions, lines would hardly ever intersect. They would only intersect at one common point an infinite number of times. Follow? Hard to put in words.

I suspect the line and point are on the same plane, and in this case only one other line would be parallel if one other point for the line in question is given.