Theorem 1. If a plane ($\pi$ ) intersects two parallel planes ($\varrho$ , $\sigma$ ), the intersection lines are parallel.

Proof. The intersection lines cannot have common points, because $\varrho$ and $\sigma$ have no such ones. Since the lines are in a same plane $\pi$ , they are parallel.

Theorem 2. If a plane ($\pi$ ) contains the normal ($n$ ) of another plane ($\varrho$ ), the planes are perpendicular to each other.

Proof. Draw in the plane $\varrho$ the line $l$ cutting the intersection line perpendicularly and cutting also $n$ . Then $l$ must be perpendicular to $n$ and thus to the whole plane $\pi$ (see the Theorem in the entry normal of plane). Consequently, the right angle formed by the lines $n$ and $l$ is the normal section of the dihedral angle formed by the planes $\pi$ and $\varrho$ . Therefore, $\pi \perp \varrho$ .