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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.

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Parallel planes

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


Figure 1Parallel 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 2Two 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 3Perpendicular 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 4Two 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.