6.3 Basic Facts About Parallel Planes Objective: recognize lines parallel to planes and skew lines Use properties relating parallel lines relating parallel.

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Presentation transcript:

6.3 Basic Facts About Parallel Planes Objective: recognize lines parallel to planes and skew lines Use properties relating parallel lines relating parallel lines and planes.

A line and plane are parallel if they do not touch.

Two planes are parallel if they do not intersect.

Skew lines : two lines are skew if they are not coplanar. (definition) two non-coplanar lines located on parallel planes are skew

NO SKEW PLANES: PLANES EITHER INTERSECT or are PARALLEL

T49: If a plane intersects two parallel planes, the lines of intersection are parallel. n n m B C D E p

Parallelism of lines and planes 1. If two planes are perpendicular to the same line, they are parallel to each other.

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.

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