# Geometry Hnrs, Chapter 10

## 23 terms

### Theorem 10-1

If a plane intersects two parallel planes, then it intersects them in two parallel lines.

### Theorem 10-2

If a line is perpendicular to one of two parallel planes it is perpendicular to the other.

### Theorem 10-3

Two planes perpendicular to the same line are parallel.

### Theorem 10-4

Two lines perpendicular to teh same plane are parallel.

### Theorem 10-5

Parallel planes are everywhere equidistant.

### Theorem 10-6

All plane angles of the same dihedral angel are congruent

### Theorem 10-7

If a line is perpendicular to a plane, then every plane contianing the line is perpendicular to the given plane.

### Theorem 10-8

If two planes are perpendicular, then any line in one of them, perpendicular to their line of intersection, is perpendicular to the other plane.

### Theorem 10-9

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.

### Corollary 10-3.1

If each of two planes is parallel to a third plane, they are parallel to each other.

### Corollary 10-4.1

A plane perpendicular to one of two || lines is perpendicular to the other.

### Corollary 10-4.2

If each of 2 lines is || to a 3rd line, then they are || to each other.

### Dihedral Angle

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.

### Edge

The line which is the dihedral angle's common edge is called the edge of the dihedral angle.

### Side/Face

The union of teh edge and either of the two half-planes of a dihedral angle is called a side, or a face.

### Plane Angle

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.

### Measure

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.

### Perpendicular

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.

### Projection

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.