Geometry - Postulates and Theorems for Points & Lines

1. Geometry 1.5 Postulates and Theorems Relating Points & Lines

2. Some Important Terms • Postulate(Post.)-a basic assumption without proof • Theorem(Thm.)-a statement that can be proved using postulates, defn.’s & previously proved thms. • Determine-to define or specify “4 walls, a ceiling, and a floor determine a room”

3. Some Important Terms • Exists-there is at least one “chairs exist in this room” • Unique-there is no more than one “In this room, the computer is unique, the chairs are not” • One and only one-exactly one; shows existence and uniqueness “In this room, there is one and only one fire extinguisher”

4. Postulate 6(Know the meaning not the number) • Through any two points there is exactly one line. • How would you write this using the word determine? Two points determine a line. A . B .

5. Postulate 7(Know the meaning not the number) • Through any three noncollinear points there is exactly one plane. • Through any three points there is at least one plane. See diagram on the board. . B . A . C

6. Postulate 8(Know the meaning not the number) • If two points are in a plane, then the line that contains the points is in the plane. B . A .

7. Postulate 9(Know the meaning not the number) • If two planes intersect, then their intersection is a line. B . A .

8. Theorem 1.1 (Know the meaning not the number) • If two lines intersect, then they intersect in exactly one(one and only one) point. The point exists(there is at least one point) and is unique(no more than one point exists). A .

9. Theorem 1.2 (Know the meaning not the number) • Through a line and a point not in the line, there is exactly one(one and only one) plane. The plane exists(there is at least one plane) and is unique(no more than one plane exists). A .

10. Theorem 1.3 (Know the meaning not the number) • If two lines intersect, then exactly one (one and only one) plane contains the lines. The plane exists(there is at least one plane) and is unique(no more than one plane exists).

11. Quick Quiz • Two points must be ___________ Collinear • Three points may be __________ Collinear • Three points must be __________ Coplanar • Four points may be __________ Coplanar

12. Quick Quiz • Three noncollinear points determine a ___ Plane • A line and a point not on a line determine a __________ Plane • A line and a plane can 1)__________ 2)_________ or 3)____________ Be Parallel, Intersect in exactly one point, or the plane can contain the line • Four noncoplanar points determine __________ Space

13. Homework • P. 21 #4-32(4X) P. 25 #1-17 Odd P. 29 S.T. #1-11 Odd • Bring Compass Tomorrow