Intersect vs Nonintersecting - What's the difference?

As a verb intersect

is to cut into or between; to cut or cross mutually; to divide into parts.

not intersecting.

(en verb)

To cut into or between; to cut or cross mutually; to divide into parts.

Parallel lines don't intersect .

Any two diameters of a circle intersect each other at the centre.

* Cowper

Lands intersected by a narrow frith / Abhor each other.

(mathematics) of two sets, to have at least one element in common

* * *

* non-intersecting

(-)

Not intersecting.

In Euclidean geometry, nonintersecting lines are always parallel.