(1) Corresponding dihedral angles have corresponding faces. Two corresponding faces are parallel half-planes lying in their hyperplane on the same side of the plane determined by the two parallel lines.
(2) Two parallel half-lines extend in the same direction when in their plane they lie on the same side of the line determined by their extremities.
(3) The proof given in our text-books that the two dihedral angles are equal does not require that the trihedral angles shall lie in one hyperplane.