The document outlines several postulates and theorems relating points, lines, and planes in geometry: Postulate 5 states that a line contains at least two points, a plane contains at least three non-collinear points, and space contains at least four points not all in one plane. Postulate 6 states that through any two points there is exactly one line. Postulate 7 states that through any three points there is at least one plane, and through any three non-collinear points there is exactly one plane. Theorems 1-1 and 1-3 state that if two lines intersect, they intersect at exactly one point and there is exactly one plane containing the lines. Theorem 1-2

1. Postulates and Theorems Relating Points, Lines, and Planes 1-5

2. Recall… 4 Postulates we’ve accepted so far: The Ruler Postulate The Protractor Postulate The Segment Addition Postulate The Angle Addition Postulate

3. More Postulates!!! Postulate 5: A line contains at least ___ points A plane contains at least ___ non collinear points space contains at least ___ points not all in one plane.

4. More Postulates!!! Postulate 6: Through any ___ points, there is exactly one line Postulate 7: Through any 3 points there is at least __ plane, and through any three non collinear points there is exactly ____ plane.

5. More Postulates!!! Postulate 8 If two points are in a plane, then the line that contains the points is in that plane. A B M

6. More Postulates!!! Postulate 9 If two planes intersect, then their intersection is a line. DC is the intersection of Plane A and Plane B A B

7. Theorems Important statements that are proved are called theorems . May be used to justify statements

8. Theorems Theorem 1-1: Intersection of lines If two lines intersect, then they intersect in exactly one point.

9. Theorems Theorem 1-2 Through a line and a point not in the line there is exactly one plane. B K A

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

11. SPICSA Pg 25, # 1 – 11, 13 - 15, 18, 19 a-d