Relationship between two lines that form a right angle or between two orthogonal planes.
Properties
- The relationship on the set of lines in the plane is symmetric, but it is neither reflexive nor transitive.
- It is symmetric : if ℓ\(_{1}\) ⊥ ℓ\(_{2}\), then ℓ\(_{2}\) ⊥ ℓ\(_{1}\).
- It is not reflexive : a line ℓ cannot be perpendicular to itself.
- It is not transitive : if ℓ\(_{1}\) ⊥ ℓ\(_{2}\) and ℓ\(_{2}\) ⊥ ℓ\(_{3}\), then ℓ\(_{1}\) // ℓ\(_{3}\).
Symbol
The symbol for the relationship of perpendicularity is “⊥” which means “is perpendicular to”.
Example
- Line ℓ\(_{1}\) is perpendicular to line ℓ\(_{2}\).
- These two planes are perpendicular: :
Note that in the case of three different planes, it is possible to have \(∏_1, ∏_2\) and \(∏_3\), with \(∏_1\) ⊥ \(∏_2\), \(∏_2\) ⊥ \(∏_3\) and \(∏_1\) ⊥ \(∏_3\). However, for three lines ℓ1, ℓ2 and ℓ3, in the same plane, it is not possible for ℓ1 ⊥ ℓ2, ℓ2 ⊥ ℓ3 and ℓ1 ⊥ ℓ3 at the same time.