a⊥α ⟺ a⊥c ∀c⊂αa\perp \alpha \iff a\perp c~~\forall c\subset \alphaa⊥α⟺a⊥c ∀c⊂α.
a,b⊥α ⟹ a∥ba,b \perp \alpha \implies a\parallel ba,b⊥α⟹a∥b.
α,β⊥a ⟹ α∥β\alpha,\beta \perp a\implies \alpha\parallel \betaα,β⊥a⟹α∥β.
A∉α ⟹ ∃! a⊥α, A∈aA\notin \alpha \implies \exists!~a\perp\alpha,~A\in aA∈/α⟹∃! a⊥α, A∈a.
a⊥α ⟸ a⊥b,c⊂α, b∩c≠∅a\perp \alpha \impliedby a\perp b,c \subset \alpha,~b\cap c\ne\varnothinga⊥α⟸a⊥b,c⊂α, b∩c=∅.
Last updated 7 days ago