1. 1.2 Points, Lines, and Planes the 3 undefined terms of Geometry

2. A Point No size, no dimensions, it only has position
A true point cannot be seen with the naked eye
Name a point with a capital letter. A
Note the dot is only a representation of a pt.

3. l Read Line AB or Line l Line
An infinite number of points that extends in 2 directions
Name a line with 2 points(2 capital letters)
Or with one lower case letter l
Read Line AB or Line l

4. limited number, terminates Collinear points points on the same line
Infinite
never ending, ongoing
Finite
limited number, terminates
Collinear points
points on the same line
Noncollinear points
points not on the same line

5. Plane
A flat surface without thickness that extends infinitely in all directions
Name a plane with one capital letter that has no point or with 3
noncollinear points E
Plane F, Plane ABC, Plane BAC, Plane DAC
or Plane CBA , etc D

6. Coplanar points
Points that lie in the same plane
Noncoplanar points
points that do not lie in the same plane

7. Postulate or Axiom
A statement that we assume is true or that we accept as fact
Theorem
A statement that must be proven true.
You use definitions, postulates and other theorems to prove theorems true.

8. Basic Postulates
2 points determine a line.
2 lines intersect in a point
2 planes intersect in a line
3 planes intersect in a point or a line
If 2 pts lie in a plane, then the plane contains every pt on the line.

9. Rectangular Prism – faces are rectangles and bases are always parallel
Diagram 1
Rectangular Prism – faces are rectangles and bases are always parallel

10. Parallel lines
Coplanar lines that never intersect
Skew lines
Noncoplanar lines that never intersect

11. 4 postulates 4 ways to determine a plane
3 noncollinear pts determine a plane
A line and a pt not on the line determine a plane
2 ll lines determine a plane
2 intersecting lines determine a plane

12. Noncoplanar points and space are the same
The set of all points
Noncoplanar points and space are the same

13. 4 noncoplanar points determine space
Postulate
4 noncoplanar points determine space
If you can make skew lines out of 4 pts, then you know you are in space.

14. Postulates
An infinite number of planes can be passed through a line.
Or a line determines an infinite number of planes.

15. Any 2 points are collinear
Any three points lie in the same plane
Only 3 noncollinear points determine one plane
Skew lines always indicate space

16. R Give a reason for each answer!!!! A,B,C E,F,C,B G,D E,F,A G,C,A,B
Determine if the following sets of points are collinear, noncollinear (coplanar), or noncoplanar (space).
A,B,C
E,F,C,B
G,D
E,F,A
G,C,A,B
F,C
D,A,R R
Give a reason for each answer!!!!

17. J
Determine if the following are collinear, coplanar, or noncoplanar.
E,D A,C
A,B,F 6. E,F,C,B
G,C,B,A 7. B,D,E,H
F,A,H,B 8. G,A
9. A, J, B

18. Postulate – the intersection of 2 planes is a line
Plane SUY ∩ Plane CSY
in SY
Diagram 2

19. Explain the relationship between 2 planes.
They intersect in a line or they are parallel.
Diagram 3

20. Give the intersection of the following:
Diagram 3
Give the intersection of the following:
Plane UXV ∩ Plane UXQ
Plane UQR ∩ Plane XWS
Plane VWS ∩ Plane XUV

21. Explain the relationship between a line and a plane.
They intersect in a pt or a line.
Diagram 4

22. Distribute Geometry Plane and Simple worksheet # 5
Allow students to work together for about 5 to 10 minutes

23. Hapless Hairline True/False
A plane is determined by 2 intersecting lines.
If 3 pts are coplanar, they are collinear.
Any 2 pts are collinear.
A plane and a line intersect at most in one pt.

24. 3 points are not always coplanar.
2 planes intersect in infinitely many pts.
2 different planes intersect in a line.
A line lies in one and only one plane.
A line and a pt not on the line lie in one and only one plane.
3 planes can intersect in only one pt.

25. 11. 3 lines can intersect in only one pt.
3 lines can intersect in only 2 points.
The intersection of any 2 half-planes is necessarily a half-plane.
The edge of a half-plane is another half-plane.

26. assign pgs. 13-15 ( 1-51 odd), (60-66 all) hw

27. Diagram 1

28. Diagram 2

29. Diagram 3

30. Diagram 4