parallel and perpendicular planes
Proof. The intersection lines cannot have common points, because and have no such ones. Since the lines are in a same plane , they are parallel.
Theorem 2. If a plane () contains the normal (http://planetmath.org/PlaneNormal) () of another plane (), the planes are perpendicular (http://planetmath.org/DihedralAngle) to each other.
Proof. Draw in the plane the line cutting the intersection line perpendicularly and cutting also . Then must be perpendicular to and thus to the whole plane (see the Theorem in the entry normal of plane). Consequently, the right angle formed by the lines and is the normal section of the dihedral angle formed by the planes and . Therefore, .
|Title||parallel and perpendicular planes|
|Date of creation||2013-04-19 15:18:51|
|Last modified on||2013-04-19 15:18:51|
|Last modified by||pahio (2872)|