## Postulates

August 18, 2023

The points on a line can be paired in a one-to-one correspondence with the real numbers such that:

1. Any two given points can have coordinates 0 and 1.
2. The distance between two points is the absolute value of the difference of their coordinates.

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

Given a point, X, on line PR, consider ray XP and ray XR as well as all the other rays that can be drawn, with X as the endpoint, on one side of line PR. These rays can be paired with the real numbers from 0 to 180 such that:

1. Ray XP is paired with 0, and ray XR is paired with 180.
2. If ray XA is paired with another number, c, and ray XB is paired with another number, d, then m<AXB = [c – d].

If point D is in the interior of angle ABC, then the m of angle ABD + the m of angle DBC = the measure of Angle ABC

Through any two points, there is exactly one line.

Through any three noncollinear points, there exists exactly one plane.

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

If two points lie on a plane, then the line containing the points lies in the plane.

A line contains at least 2 points. A plane contains at least 3 noncollinear points. Space contains at least 4 noncoplanar points.

Through a point not on a line, there exists exactly one line through the point that is parallel to the line.