More Non-Euclidean Geometry

Find out if these statements remain true under the non-Euclidean geometry.
Theorem: The perpendiculars dropped upon the sides of a triangle from the  projections of the opposite vertices upon a given line are concurrent.
Definition: This point is called the orthopole of the given line with respect to the given triangle.
 
Pole and polar with respect to a triangle.
Isogonal conjugate.
 
Simson line.