Plane
From AoPSWiki
In mathematics, a plane is a two-dimensional object that is infinitely long and wide, but has no thickness and zero curvature.
Euclidean Geometry
In Euclidean geometry, a plane is defined by:
- three non-collinear points
- a line and a point not on the line
- two intersecting lines
- two parallel lines
Properties
A line can intersect a plane in a single point, or it can be in the plane.
Two planes perpendicular to the same line are parallel to eachother.
Two lines perpendicular to the same plane are parallel to eachother.
Two planes can be parallel, or they can intersect in a line.
If two lines are perpendicular to eachother and one of them is in a plane, the other is perpendicular to the plane.
See Also
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