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 : ℓ\(_{1}\) // ℓ\(_{1}\).
- It is reflexive : if ℓ\(_{1}\) // ℓ\(_{2}\), then ℓ\(_{2}\) // ℓ\(_{1}\).
- It is transitive : if ℓ\(_{1}\) // ℓ\(_{2}\) and ℓ\(_{2}\) // ℓ\(_{3}\), then ℓ\(_{1}\) // ℓ\(_{3}\).
Examples
- The lines ℓ\(_{1}\) and ℓ\(_{2}\) are parallel.
The lines ℓ\(_{3}\) and ℓ\(_{4}\) are parallel.
- The planes ∏\(_{1}\) and ∏\(_{2}\) are parallel planes.
