# Relationship of Parallelism

## Relationship of Parallelism

Relationship on the set of lines in the plane or between planes that is symmetric, reflexive and transitive.

### Symbol

The symbol for the relationship of parallelism is “//”, which means “is parallel to”.

### Properties

The relationship of parallelism has the following properties :

• It is symmetric : $$_{1}$$ // $$_{1}$$.
• It is reflexive : if $$_{1}$$ // $$_{2}$$, then $$_{2}$$ // $$_{1}$$.
• It is transitive : if $$_{1}$$ // $$_{2}$$ and $$_{2}$$ // $$_{3}$$, then $$_{1}$$ // $$_{3}$$.

### Examples

• The lines $$_{1}$$ and $$_{2}$$ are parallel.
The lines $$_{3}$$ and $$_{4}$$ are parallel.
• The planes ∏$$_{1}$$ and ∏$$_{2}$$ are parallel planes.