Geometry Help: Points, Lines, and Planes

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.

Source

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.

Source

Postulate 3

If any two planes intersect, then they intersect in exactly one line.

Source

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.

Source

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
  • when naming a plane, use at least 3 points given as vertices in the diagram, or use a point on the interior

More On Geometry

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