1. Lesson 2.1
Subsets of Lines pp

2. Objectives:
1. To define important subsets of lines.
2. To apply the Line Separation Postulate.
3. To use correct notation for subsets of lines.

3. Definition
A half-line is the set of all points on a line on a given side of a given point of the line.

4. A half-line does not include the
point from which the half-line originates.
Denoted: AB

5. Postulate 2.1
Line Separation Postulate.
Every point divides any line through that point into three disjoint sets: the point and two half-lines.

6. Definition
A ray is the union of a half-line and its origin. It extends infinitely in one direction from a point.

7. A ray includes the point from which it originates.
Denoted: AB

8. The endpoint is always written first when naming a ray.
Denoted: AB

9. Example: Refer to the figure to find XY  {X}. 1. { } 2. X 3. XY 4. XY
1. { }
2. X
3. XY
4. XY W X Y Z

10. Example: Refer to the figure to find XY  YZ. 1. XY 2. YZ 3. XY 4. XYW X Y Z

11. Example 1: Name five different lines.K L M E D B H I J C G F P N
Example 1: Name five different lines.

12. Example 2: Give two other names for ID.K L M E D B H I J C G F P N
Example 2: Give two other names for ID.

13. Example 3: Name six rays on KP.D B H I J C G F P N
Example 3: Name six rays on KP.

14. Example 4: Name six half-lines with endpoint B.K L M E D B H I J C G F P N
Example 4: Name six half-lines with endpoint B.

15. Example 5: Name five half-lines containing B.K L M E D B H I J C G F P N
Example 5: Name five half-lines containing B.

16. Homework pp

17. ►A. Exercises
Use the figure below for exercises 4-10. A B C D
5. How many sets are formed on AD by the point C? Name them.

18. ►A. Exercises
Use the figure below for exercises 4-10. A B C D
7. Explain why BC and BD are the same ray.

19. ►A. Exercises
Use the figure below for exercises 4-10. A B C D
7. Explain why BC and BD are the same ray.

20. ►A. Exercises
Use the figure below for exercises 4-10. A B C D
9. Name AC in two other ways.

21. ►B. Exercises
Use the figure below for exercises A B C D
11. Find AB  {A}
= AB

22. ►B. Exercises
Use the figure below for exercises A B C D
13. CD  CA
= { }

23. ►B. Exercises
Use the figure below for exercises A B C D
15. AC  BC
= BC

24. ►B. Exercises
Use the figure below for exercises A B C D
17. BD  CA
= AD

25. 20. Name as many rays as possible in the figure.
►C. Exercises
20. Name as many rays as possible in the figure. A I H B G F C D E

26. ■ Cumulative Review
Identify the undefined term best illustrated in each example.
21. a piece of paper

27. ■ Cumulative Review
Identify the undefined term best illustrated in each example.
22. an electron

28. ■ Cumulative Review
Identify the undefined term best illustrated in each example.
23. a crease in a garment

29. ■ Cumulative Review
Identify the undefined term best illustrated in each example.
24. a ramp for loading a truck

30. ■ Cumulative Review
Identify the undefined term best illustrated in each example.
25. a pixel (smallest dot on a computer
screen)