A line a is parallel to the plane of projection Π
and perpendicular to the line b. We need to prove that
their projections are also perpendicular, i.e. a' ⊥ b'. (Line a is parallel to the plane Π, while z is perpendicular to Π.) Proof can be written as: a ⊥ b & a   Π => a ⊥ E => a' ⊥ E => a' ⊥ b'. 
n ⊥ P <=> p' ⊥ r_{1} & p'' ⊥ r_{2}.
T ∈ Σ<=>d(A,T) = d(B,T) 

The normal line and the1st steepest line through the pedal of the normal lie in the same horizontal projecting plane.  The normal line rotated into the plane Π_{1} is perpendicular to the 1st steepest line rotated as well, they intersect at the projection of the pedal. 
The normal line and the 2st steepest line through the pedal of the normal lie in the same vertical projecting plane.  The normal line rotated into the plane Π_{2} is perpendicular to the 2st steepest line rotated as well, they intersect at the projection of the pedal. 
Created by Sonja Gorjanc, translated by Helena Halas and Iva Kodrnja  3DGeomTeh  Developing project of the University of Zagreb