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