Lesson 2.1 Subsets of Lines pp. 42-44

1. Lesson 2.1 Subsets of Lines pp. 42-44

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

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

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

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

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

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

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

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

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

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

16. Homeworkpp. 43-44

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

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

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

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

21. A B C D = AB 11. Find AB  {A} ►B. Exercises Use the figure below for exercises 11-18.

22. A B C D 13. CD  CA ►B. Exercises Use the figure below for exercises 11-18. = { }

23. A B C D 15. AC  BC = BC ►B. Exercises Use the figure below for exercises 11-18.

24. A B C D 17. BD  CA = AD ►B. Exercises Use the figure below for exercises 11-18.

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

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)