Postulates and Theorems beginning with P

Postulates and Theorems
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Postulate 1
A line contains at least two points.
Postulate 10

If OB lies between OA and OC, then m AOB + m BOC = m AOC.

Postulate 2
A plane contains at least 3 non-collinear points.
Postulate 3

Through any two points, there is exactly one line.

Postulate 4
Through any three non-collinear points, there is exactly one plane.
Postulate 5
If two points lie in a plane, then the line joining them lies in that plane.
Postulate 6

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

Postulate 7
Each point on a line can be paired with exactly one real number called its coordinate. The distance between two points is the positive difference of their coordinates.
Postulate 8

If B lies between A and C on a line, then AB + B+C = AC

Postulate 9

Suppose O is a point on XY. Consider all rays with endpoint O that lie on one side of XY. Each ray can be paired with exactly one real number between 0º and 180º. The positive difference between two numbers representing two different rays is the measure of the angle whose sides are the two rays.