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.

Through a line and a point not

in the line there is exactly one plane.

If two lines intersect, then

exactly one plane contains the lines.

A rule we accept without a proof.

An important rule that is proved.

1. The points on a line can be paired with the real numbers in such a

way that any two points can have coordinates 0 and 1.

2. Once a coordinate system as been chosen in this way, the

distance between any two points equals the absolute value of the

difference of their coordinates.

length of a segment = $$\left|x_2-x_1\right|$$  

1. If B is between A and C, then

AB + BC = AC.

2. If AB + BC = AC, then B is between

A and C.

On line $$\overleftarrow{A}\overrightarrow{B}$$   in a given plane, choose any point O between A

and B. Consider $$\overrightarrow{OA}$$ and $$\overrightarrow{OB}$$ and all the rays that can be drawn

from O on one side of $$\overleftarrow{A}\overrightarrow{B}$$ . These rays that can be paired with

the real numbers from 0 to 180 in such a way that:

a) $$\overrightarrow{OA}$$ is paired with 0, and $$\overrightarrow{OB}$$ with 180.

b) If $$\overrightarrow{OP}$$  is paired with x, and $$\overrightarrow{OQ}$$  with y, then $$m\angle POQ=\left|x-y\right|$$  

Part 1: If point B lies in the interior of ∠AOC, then

m∠AOB + m∠BOC = m∠AOC.

Part 2: If ∠AOC is a straight angle and B is any

point not on AC, then

m∠AOB + m∠BOC = 180.