Relationship of Perpendicularity

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[latex]_{1}[/latex] ⊥ ℓ[latex]_{2}[/latex], then ℓ[latex]_{2}[/latex] ⊥ ℓ[latex]_{1}[/latex].
It is not reflexive : a line ℓ cannot be perpendicular to itself.
It is not 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].

Symbol

The symbol for the relationship of perpendicularity is "⊥" which means "is perpendicular to".

Example

Line ℓ[latex]_{1}[/latex] is perpendicular to line ℓ[latex]_{2}[/latex].

These two planes are perpendicular: :

Note that in the case of three different planes, it is possible to have [latex]∏_1, ∏_2[/latex] and [latex]∏_3[/latex], with [latex]∏_1[/latex] ⊥ [latex]∏_2[/latex], [latex]∏_2[/latex] ⊥ [latex]∏_3[/latex] and [latex]∏_1[/latex] ⊥ [latex]∏_3[/latex]. 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.

Relationship of Perpendicularity

Properties

Symbol

Example

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