A plane goes on forever, so we can't really draw one. But we can draw a square piece of a plane to illustrate some of the postulates and theorems about planes. Here are the main facts:
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(1) |
The intersection of two planes is a line: |
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(2) |
Three noncollinear points determine a plane: |
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(3) |
A line and a point not on that line determine a plane: |
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(4) |
Two intersecting lines determine a plane: |
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(5) |
The intersection of a line and a plane not containing that line is a point: |
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(6) |
If a plane contains two points, then it contains the line through those two points. |
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(7) |
It is possible for three or more planes to intersect in a line: |
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(8) |
It is possible for three planes to intersect in a point: |
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(9) |
It is possible for three noncoplanar lines to intersect in a point: |
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Date last modified: September 8, 2008.
