# Parallel

In two-dimensional Euclidean space, two lines that do not intersect are said to be parallel. In three-dimensional Euclidean space, parallel lines not only fail to intersect, but also maintain a constant separation between points closest to each other on the two lines.

Parallel is an elementary-school-level concept. It is listed in the California State Standards for Grade 3.

### Prerequisites

Intersection: | (1) In set theory, the intersection of two or more sets is the set of elements common to all sets. (2) In geometry, the intersection of two or more regions is the region that is common to all regions. |

Line: | A line is the infinite extension in both directions of a line segment, giving the path of shortest distance between two points in Euclidean space. |