1. Basic Postulates in Geometry Mrs. Lee Dr. Koroleva August 2006 The Preuss School UCSD

2. PostulateExample Non- Example Diagram In your notes start a table as shown.

3. PostulateExample Non- Example Diagram Point-Line-Plane Postulate a. Unique Line Assumption Through any two points, there is exactly one line.

4. PostulateExample Non- Example Diagram Point-Line-Plane Postulate b. Number Line Assumption Every line is a set of points that can be put into a one- to-one correspondence with the real numbers, with any point on it corresponding to 0 and any other point corresponding to 1.

5. PostulateExample Non- Example Diagram Point-Line-Plane Postulate c. Dimension Assumption 1) Given a line in a plane, there is at least one point in the plane that is not on the line. 2) Given a plane in a space, there is at least one point in space that is not in the plane.

6. PostulateExample Non- Example Diagram Line Intersection Theorem Two different lines intersect in at most one point.

7. PostulateExample Non- Example Diagram Definition of Parallel Lines Two coplanar lines m and n are parallel lines, written m||n, if and only if they have no points in common or they are identical.

8. PostulateExample Non- Example Diagram Distance Postulate a. Uniqueness Property On a line, there is a unique distance between two points.

9. PostulateExample Non- Example Diagram Distance Postulate b. Distance Formula If two points on a line have coordinates x and y, the distance between them is |x-y|.

10. PostulateExample Non- Example Diagram Distance Postulate c. Additive Property If B is on, then AB+BC=AC.