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
Drag any orange dot at the points P or Q. As the line
moves, the line
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.
To show that lines are parallel, we draw small arrow marks on them.
In the figure above, note the arrows on the lines
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.
When we write about parallel lines there is a shorthand we can use. We can write
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.
In a very similar way,
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
where the two bases (ends) are always parallel to each other.
Other parallel topics
Angles associated with parallel lines
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