Relationship of Perpendicularity

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 $$_{1}$$ ⊥ $$_{2}$$, then $$_{2}$$ ⊥ $$_{1}$$.
• It is not reflexive : a line  cannot be perpendicular to itself.
• It is not transitive : if $$_{1}$$ ⊥ $$_{2}$$ and $$_{2}$$ ⊥ $$_{3}$$, then $$_{1}$$ // $$_{3}$$.

Symbol

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

Example

• Line $$_{1}$$ is perpendicular to line $$_{2}$$.

• 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 12 and 3, in the same plane, it is not possible for 1 ⊥ 22 ⊥ 3 and 1 ⊥ 3 at the same time.