1. Relating Points, Lines, and Planes

2. Key words THEOREMS: statements that can be proved. THEOREMS: statements that can be proved. POSTULATE: statements that cannot be proved. POSTULATE: statements that cannot be proved.

3. So what? Just like Geometry started with three undefined terms (what are they?), it also had to start with five “unproved” postulates. Just like Geometry started with three undefined terms (what are they?), it also had to start with five “unproved” postulates. From these five postulates come all geometric theorems. From these five postulates come all geometric theorems. They are the foundation for Geometry! They are the foundation for Geometry!

4. Postulate 5 A line contains at least two points; A line contains at least two points; a plane contains at least three points; a plane contains at least three points; space contains at least four points not all in one plane. space contains at least four points not all in one plane.

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

6. Postulate 7 Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane. Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane.

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

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

9. Now its time for the THEOREMS!!!!!

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

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

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

13. PRACTICE Page 24 Page 24 #4 – 16 #4 – 16

14. Check this out. Check this out.out