Parallel (geometry) facts for kids
Parallel is a term in geometry and in everyday life that refers to a property of lines or planes. Parallel lines or planes are next to each other, but never touch each other. This means they never intersect at any points. The slopes of parallel lines are always equal.
See how even if these two line segments were extended to infinity, there would never be a point of intersection between the two of them.
Construction
Images for kids

On the sphere there is no such thing as a parallel line. Line a is a great circle, the equivalent of a straight line in spherical geometry. Line c is equidistant to line a but is not a great circle. It is a parallel of latitude. Line b is another geodesic which intersects a in two antipodal points. They share two common perpendiculars (one shown in blue).

Intersecting, parallel and ultra parallel lines through a with respect to l in the hyperbolic plane. The parallel lines appear to intersect l just off the image. This is an artifact of the visualisation. It is not possible to isometrically embed the hyperbolic plane in three dimensions. In a real hyperbolic space the lines will get closer to each other and 'touch' in infinity.