Geometry - Postulates and Theorems - Chapter 1

What does the expansion postulate state?

• A line contains at least two points

• A plane contains at least three noncollinear points

• Space contains at least four noncoplanar points

What does the line postulate state?

Any two points in space lie in exactly one line

What does the plane postulate state?

Three noncollinear points lie in exactly one plane

What does the flat plane postulate state?

If two points lie in a plane, then the line containing those two points lies in the same plane

What does the plane intersection postulate state?

If two planes intersect, then their intersection is exactly one line

A line and a point not on that line are. . .

Contained in one and only one plane

Two intersecting lines are contained in. . .

One and only one plane

Two parallel lines are contained in. . .

One and only one plane

What does the line separation postulate state?

Every point on a line divides the line into three disjoint sets: the point and two half-lines

What does the plane separation postulate state?

Every line in a plane divides the plane into three disjoint sets: the line and two half-planes