Lines Parallel to Planes, Parallel Planes, Skew Lines

Definition-A line and a plane are parallel if they do not intersect.

Definition-Two planes are parallel if they do not intersect.

Definition-Two lines are skew if they are not coplanar.

Theorem-f a plane intersects two parallel planes, the lines of intersection are parallel.

Properties Relating Parallel Lines and Planes

1. If two planes are perpendicular to the same line, they are parallel.


2. If a line is perpendicular to one of two parallel planes, it is perpendicular to the other plane as well.


3. If two planes are parallel to the same plane, they are parallel to each other.


4. If two lines are perpendicular to the same plane, they are parallel to each other.


5. If a plane is perpendicular to one of two parallel lines, it is perpendicular to the other line as well.