You might be tempted come think the planes together vehicles to be uncovered up in the sky or in ~ the airport. Well, remainder assured, geometry is no fly‐by‐night operation.
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Parallel planes
Parallel planes room two planes that do not intersect. In number 1, airplane P // airplane Q.
Theorem 11: If every of two planes is parallel come a 3rd plane, then the 2 planes room parallel to each other (Figure 2).
Figure 2Two plane parallel to a 3rd plane
Perpendicular planes
A heat l is perpendicular to aircraft A if l is perpendicular to all of the currently in aircraft A that crossing l. (Think of a rod standing straight up ~ above a level surface. The stick is perpendicular to every one of the lines drawn on the table that pass with the suggest where the rod is standing).
A airplane B is perpendicular come a plane A if plane B includes a line the is perpendicular to aircraft A. (Think the a book well balanced upright top top a level surface.) See figure 3.
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Figure 3Perpendicular planes
Theorem 12: If two planes room perpendicular come the same plane, then the 2 planes either intersect or room parallel.
In figure 4, plane B ⊥ aircraft A, aircraft C ⊥ plane A, and airplane B and plane C intersect along line l.
Figure 4Two intersecting plane that are perpendicular come the exact same plane
In figure 5, plane B ⊥ airplane A, aircraft C ⊥ airplane A, and aircraft B // aircraft C.