Postulates 1-9 theorems 1-1, 1-2, 1-3

Theorem 1-2

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

Postulate 2(Segment Addition Postulate)

If B is between A & C, then AB + BC = AC

Postulate 8

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

Postulate 6

Through any two points there is exactly one line

Postulate 5

A line contains at least two points; a plane contains at least three points not all in one line; space contains at least four points not all in one plane

Postulate 4(angle Addition postulate)

If point B lies in the interior of (angle) AOC, then (measure of angle)AOB+(measure of angle)BOC=(measure of angle)AOC. If (angle) AOC is a straight angle and B is any point not on (line) AC, then the (measure of angle)AOB+(measure of angle)BOC=180.

Theorem 1-3

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

Theorem 1-1

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

Postulate 3(Protractor Postulate)

On (line) AB in a given plane, choose any point O between A and B. Consider (ray) OA and (ray) OB and all the rays that can be drawn from O on one side of (line) AB. These rays can be paired with the real numbers from 0 to 180 in such a way that: a. (ray) OA is paired with 0, and (ray) OB with 180. b. If (ray) OP is paired with x, and (ray) Oq with y, then (measure of angle) POQ= abs(x-y)

Postulate 1 (Ruler Postulate)

The points on a line can be paired with the real numbers in such a way that any two points can have coordinates 0 & 1. Once a coordinate system has been chose in this way, the distance between any two points equals the absolute value of the difference of their coordinates.

Postulate 7

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

Postulate 9

If two planes intersect, then their intersection is a line