Parallel
From Greek: para allelois "beside one another"
Lines are parallel if they lie in the same plane, and are the same distance apart over their entire length
Try this Drag any orange dot at the points P or Q. As the line
PQ
moves, the line
RS
will remain parallel to it.

Parallel lines remain the same distance apart over their entire length. No matter how far you extend them, they will never meet.

The arrows

To show that lines are parallel, we draw small arrow marks on them. In the figure above, note the arrows on the lines
PQ
and
RS
. This shows that these lines are parallel. If the diagram has another set of parallel lines they would have two arrows each, and so on.

Shorthand notation

When we write about parallel lines there is a shorthand we can use. We can write
PQ
||
RS
. which is read as "the line PQ is parallel to the line RS".

Constructing a parallel line

In the Constructions chapter, there is an animated demonstration of how to construct a line parallel to another that passes through a given point, using only a compass and straightedge. See Constructing a parallel line through a point.

Parallel planes

In a very similar way, planes can be parallel to each other also. It means that the two planes are the same perpendicular distance apart everywhere. So, for example, the cards in a deck of cards are parallel.

An example of this is a cylinder, where the two bases (ends) are always parallel to each other.

Other parallel topics

General

Angles associated with parallel lines

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