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.Relation de parallélisme
  • The planes ∏\(_{1}\) and ∏\(_{2}\) are parallel planes.

Relation de Parallélisme-B

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