Geometry Help: Points, Lines, and Planes
Published by An explanation of points, lines, and planes.
Definition: Postulate
A postulate, or axiom, is an accepted statement of fact. It cannot be proved. This means that everyone believes it is true, but there is no way to prove it.
Postulate 1
Through any two points there is exactly one line.
This means that if you have two points in space you can draw a line connecting them. There is no way to draw more than one line through them.
As you can see, there is only one possible way to draw a line in between the two points.
Postulate 2
If any two lines intersect, they create exactly one point.
As you see below, line HI and line JK intersect in one and only one point.
Postulate 3
If any two planes intersect, then they intersect in exactly one line.
Plane A and plane B are intersecting planes. They intersect at line KI.
Postulate 4
Through any three noncollinear points, there is exactly one plane.
A, B, and C are noncollinear points, meaning that if you connected the dots, they would not make a straight line. Therefore, they form one plane.
More About Planes
- planes extend out forever and ever
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when naming a plane, use at least 3 points given as vertices in the diagram, or use a point on the interior
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