You may be tempted to think of planes as vehicles come be found up in the skies or at the airport. Well, rest assured, geometry is no fly‐by‐night operation.

You are watching: Two planes that do not intersect

**Parallel planes**

**Parallel planes** are two plane that execute not intersect. In figure 1, aircraft *P* // plane *Q*.

**Figure 1**Parallel planes

Theorem 11: If each of two planes is parallel to a 3rd plane, then the 2 planes space parallel to each other (Figure 2).

**Figure 2**Two planes parallel come a 3rd plane

## Perpendicular planes

A heat *l* is perpendicular to aircraft *A* if *l* is perpendicular to all of the lines in aircraft *A* that crossing *l*. (Think of a pole standing directly up ~ above a level surface. The stick is perpendicular to every one of the lines drawn on the table the pass through the point where the pole is standing).

A plane *B* is perpendicular to a airplane *A* if airplane *B* contains a line that is perpendicular to airplane *A*. (Think of a book well balanced upright on a level surface.) See figure 3.

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**Figure 3**Perpendicular planes

*Theorem 12:* If 2 planes room perpendicular to the very same plane, then the two planes either intersect or room parallel.

In number 4, airplane *B* ⊥ airplane *A*, airplane *C* ⊥ aircraft *A*, and aircraft *B* and aircraft *C* intersect follow me line *l*.

**Figure 4**Two intersecting planes that space perpendicular to the exact same plane

In figure 5, aircraft *B* ⊥ airplane *A*, plane *C* ⊥ airplane *A*, and airplane *B* // plane *C*.