Difference between revisions of "Plane"
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| − | In [[mathematics]], a '''plane''' is a two-[[dimension]]al object that is infinitely [[length | long]] and wide, but has | + | In [[mathematics]], a '''plane''' is a two-[[dimension]]al object that is infinitely [[length | long]] and wide, but has no [[thick]]ness and zero curvature. |
== Euclidean Geometry == | == Euclidean Geometry == | ||
| Line 11: | Line 11: | ||
A line can intersect a plane in a single point, or it can be in the plane. | 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 | + | Two planes [[perpendicular]] to the same line are parallel to each other. |
| − | Two lines perpendicular to the same plane are parallel to | + | Two lines perpendicular to the same plane are parallel to each other. |
Two planes can be parallel, or they can intersect in a line. | Two planes can be parallel, or they can intersect in a line. | ||
| − | If two lines are perpendicular to | + | If two lines are perpendicular to each other and one of them is in a plane, then the other is either also in that plane or perpendicular to the plane. |
== See Also == | == See Also == | ||
* [[Hyperplane]] | * [[Hyperplane]] | ||
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| + | [[Category:Definition]] | ||
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| + | [[Category:Geometry]] | ||
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| + | {{stub}} | ||
Latest revision as of 13:52, 2 October 2023
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 each other.
Two lines perpendicular to the same plane are parallel to each other.
Two planes can be parallel, or they can intersect in a line.
If two lines are perpendicular to each other and one of them is in a plane, then the other is either also in that plane or perpendicular to the plane.
See Also
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