Parallel and perpendicular lines are sets of lines which display a specific relationship between them. Parallel lines are lines that do not intersect and the perpendicular lines intersect at right angles. The following diagram shows the locations of the houses of three friends.

Parallel and Perpendicular Lines


It can be seen that Cindy's and Rudy's houses are situated in parallel streets, while Nancy's house is on a street which is perpendicular to both these streets. This illustrates how the relationship of two lines to a third line can lead to the relationship between the two lines.
1. In a plane if two lines are perpendicular to the same line, then they are parallel to each other.
2. If two lines are parallel to the same line, then they are parallel to each other.

Parallel lines are coplanar lines that have no points in common or have all points in common.
The parallel relationship is denoted by the symbol ||.In the first case, when the two lines have no points in common, we have two distinct and parallel lines. In the diagram shown below lines 'l' and 'm' are parallel lines with no common point.

Parallel Lines

If two lines under consideration have all points in common, then two lines coincide.

Parallel lines are necessarily coplanar. Non coplanar lines in space without common points are called skew lines.