Question

Why "Two non-intersecting lines are always parallel" is a wrong statement

Answer 1

In a two dimensional Euclidean plane, non-intersecting lines necessarily parallel but in three dimensional plane, there are skew lines. Two lines in three-dimensional space which do not meet must be in a common plane to be considered parallel; otherwise they are called skew lines.

Also, on curved plane where non intersecting lines may not be parallel and even parallel lines can intersect. Most popular example of curved plane- a sphere. Two lines(which meet themselves due to curvature) may not be parallel. But even two parallel lines may intersect on a sphere like two meridians on the globe intersect at the poles.

Hence, "Two non intersecting lines are always parallel" is a wrong statement.