1. Lesson 2.3
Subsets of planes pp

2. Objectives:
1. To state the Plane Separation Postulate.
2. To define various subsets of the plane.

3. Postulate 2.2
Plane Separation Postulate. Every line divides any plane containing the line into three disjoint sets: the line and two half-planes.

4. Definition
A half-plane is a subset of a plane consisting of all points on a given side of a line in the plane. If points P and Q are in the same half-plane, then so is the segment joining them.

5. Definition
An edge of a half-plane is the line that separates the plane into two half-planes. The line is not part of either half-plane.

6. Definition
Opposite half-planes are the two half-planes that are separated by a particular line of the plane. If points P and R are in opposite half-planes, the segment joining them must intersect the edge.

7. P ƒ h2 Q h1 R m

8. Definition
An angle is the union of two distinct rays with a common endpoint.
The sides of an angle are two rays that form the angle.

9. Definition
The vertex of an angle is the common endpoint (origin) of the two rays.

10. A B C

11. Definition
The interior of an angle is the intersection of the two half-planes each determined by a side of the angle and each containing the other side (except for the vertex).

12. C D p E

13. C D p E

14. Definition
The exterior of an angle is the complement of the union of the angle and its interior.

15. m h2 h1 ƒ
h1  ƒ = Ø

16. m h2 h1 ƒ
(h1  h2)′ = ƒ

17. C F D E B A G
Practice: E is in the interior of what angle?
ABF

18. C F D E B A G
Practice: BC is a side of what angles?
CBG and FBC

19. C F D E B A G
Practice: Name four angles with vertex D.
GDE, EDF, FDC, & GDC

20. C F D E B A G
Practice: Name points in the exterior of BCD.
G and F

21. Homework pp

22. C B D p A E ►A. Exercises Use the figure shown for exercises 1-2.
1. Name two sets of collinear points. p E C D B A

23. C B D p A E ►A. Exercises 2. Describe two pairs of half-planes and
give the lines that determine them. p E C D B A

24. Use the angle in the figure for ex. 3-8.
►A. Exercises
Use the angle in the figure for ex. 3-8. D A B C F E H K I G J
3. Name the angle.

25. Use the angle in the figure for ex. 3-8.
►A. Exercises
Use the angle in the figure for ex. 3-8. D A B C F E H K I G J
5. Name three points on the exterior of
the angle.

26. Use the angle in the figure for ex. 3-8.
►A. Exercises
Use the angle in the figure for ex. 3-8. D A B C F E H K I G J
7. Name the sides of the angle.

27. s1 k s2 C ►A. Exercises Use the next figure for exercises 9-15.
9. Name the two half-planes.

28. s1 k s2 C ►A. Exercises Use the next figure for exercises 9-15.
11. Find s1  s2  k.

29. s1 k s2 C ►B. Exercises Use the next figure for exercises 9-15.
13. Find s1  k.

30. s1 k s2 C ►B. Exercises Use the next figure for exercises 9-15.
15. Find (s2  k)′.

31. Use the figure for exercises 16-23.
►B. Exercises
Use the figure for exercises 1 2 3 F A B C D E
17. Name a point in the
interior of CFE.

32. Use the figure for exercises 16-23.
►B. Exercises
Use the figure for exercises 1 2 3 F A B C D E
19. Name three points on
the interior of AFE.

33. Use the figure for exercises 16-23.
►B. Exercises
Use the figure for exercises 1 2 3 F A B C D E
21. Find 1  3.

34. Use the figure for exercises 16-23.
►B. Exercises
Use the figure for exercises 1 2 3 F A B C D E
23. Name three angles that
have FA as a side.

35. ■ Cumulative Review
Use the diagram to decide whether each statement is true or false.
26. AB  AB r l A B Q C

36. ■ Cumulative Review
Use the diagram to decide whether each statement is true or false.
27. B  AB r l A B Q C

37. ■ Cumulative Review
Use the diagram to decide whether each statement is true or false.
28. A  l r l A B Q C

38. ■ Cumulative Review
Use the diagram to decide whether each statement is true or false.
29. CQ  r r l A B Q C

39. ■ Cumulative Review
Use the diagram to decide whether each statement is true or false.
30. l  r r l A B Q C