Postulates and theorems relating points, lines, and planes1.5

Theorems vs. Axioms or postulates

Theorems are rules or statements, similar to axioms or postulates. Theorems, however, are proven to be true. Throughout this course, we will look at some proofs, and make some of our own.

We are going to look at each one carefully.

A line contains at least two points,A plane contains at least three points, And space contains at least four points not all in one plane.

Through any two points, there is exactly one line.

Through any three points, there is at least one plane, and through any three noncollinear points there is exactly one plane.

If two points are in a plane, then the line that contains the points is in that plane.

If two planes intersect, then their intersection is a line.

If two lines intersect, then they intersect in exactly one point .

Theorem

Through a line and a point not on the line there is exactly one plane.

Theorem

If two lines intersect, then exactly one plane contains the lines.

Theorem