Dihedral Angle

A line on a plane divides the plane into two parts, each called a half-plane. As shown in the figure, when the two half-planes and share a common line , the following holds:

1. A figure formed by the two half-planes and is called a dihedral angle.
2. The line is referred to as the edge of the dihedral angle, and the two half-planes and are called the faces of the dihedral angle.
3. If a point on the line is taken, and two rays and perpendicular to are drawn in the half-planes and , the angle is constant regardless of the position of point . This constant angle is called the magnitude of the dihedral angle.
4. When two different planes intersect, they form four dihedral angles. Generally, the smaller of these angles is considered the angle between the two planes.
5. Specifically, when the angle between two planes and is a right angle, the two planes are said to be perpendicular, denoted by .

Angle Between a Line and a Plane

Let line meet the plane at point . Let be a point on line , and let be the foot of the perpendicular from to the plane . The angle is defined as the angle between the line and the plane .