1. Section 1-5 Postulates and Theorems Relating Points, Rays and Planesby
Nick Kramer

2. Goal
Use symbols for Lines, Segments, Rays and Distances; Find Distances.
Name the Angles and Find their Measurement.
State and Use The Segments Addition Postulate and The Angle Addition Postulate.
Recognize what you can conclude from a Diagram.
Use the Postulates and Theorems relating Points, Lines and Planes.

3. Postulates
A postulate is an assumed relationship that is seen in the world around us.
They are not always reversible

4. Postulate 5
A line contain at least two (2) points; A Plane contains at least three points not all in one line; Space contains at least four points not all in one plane.

8. Postulate 6
Through any two points there is exactly one line.

12. Postulate 7
Through any three points three is at least one plane; through any three noncollinear points there is exactly one plane.

15. Postulate 8
If two points are in a plane, then the line that contains the points is in that plane.

17. Postulate 9
If two planes intersect, then their intersection is a line

19. Theorems
A theorem is statements that can be shown to be true by a logical progression of preexisting definitions, postulates, and theorems.

20. Proving a Theorem
Proving a theorem is the process of showing the validity of a theorem

21. Theorem 1-1
If two lines intersect, then they intersect in exactly one point.

23. Theorem 1-2
Through a line and a point not in the line there is exactly one plane.

24. Theorem 1-2

25. Theorem 1-3
If two lines intersect, then exactly one plane contains the lines.

26. Theorem 1-3