If a plane intersects two parallel planes, then it intersects them in two parallel lines.
If a line is perpendicular to one of two parallel planes it is perpendicular to the other.
Two planes perpendicular to the same line are parallel.
Two lines perpendicular to teh same plane are parallel.
Parallel planes are everywhere equidistant.
All plane angles of the same dihedral angel are congruent
If a line is perpendicular to a plane, then every plane contianing the line is perpendicular to the given plane.
If two planes are perpendicular, then any line in one of them, perpendicular to their line of intersection, is perpendicular to the other plane.
If a line and a plane are not perpendicular, then the projection of the line into a plane is a line.
Two planes, or a plane and a line, are || if they do not intersect.
If each of two planes is parallel to a third plane, they are parallel to each other.
A plane perpendicular to one of two || lines is perpendicular to the other.
If each of 2 lines is || to a 3rd line, then they are || to each other.
If two half-planes have the same edge, but do not lie in the same plane, then the union of the two half-planes and their common edge is a dihedral angle.
The line which is the dihedral angle's common edge is called the edge of the dihedral angle.
The union of teh edge and either of the two half-planes of a dihedral angle is called a side, or a face.
Given a dihedral angle, and a plane perpendicular to its edge. The intersection of the perpendicular plane with the dihedral angle is called a plane angle of the dihedral angle.
The measure of a dihedral angle is the real number which is the measure of each of its plane angles.
Right Dihedral Angle
A right dihedral angle is one who plane angles are right angles.
Two planes are perpendicular if they contain a right dihedral angle.
Projection of a Point
The projection of a point into a plane is the foot of teh perpendicular from the point to the plane.
Projection of a Line
The projection of a lien into a plane is the set of all points of the plane which are projections of pointso f the line.
If A is any set of points in space, and E is a plane, then the projection of A into E is the set of all points which are projectsion of points of A into E.