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Lesson 2.2 Betweenness pp. 45-47

Lesson 2.2 Betweenness pp. 45-47. Objectives: 1. To define betweenness of points. 2. To define more subsets of lines. 3. To apply correct notation to the new geometric terms. B is between A and C if BC  BA = {B} when A, B, and C are collinear. In symbols, you can write A-B-C.

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Lesson 2.2 Betweenness pp. 45-47

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  1. Lesson 2.2 Betweenness pp. 45-47

  2. Objectives: 1. To define betweenness of points. 2. To define more subsets of lines. 3. To apply correct notation to the new geometric terms.

  3. B is between A and C if BC  BA = {B} when A, B, and C are collinear. In symbols, you can write A-B-C. Definition

  4. A B C In order for B to between A and C, all three points must be collinear!

  5. If C is between A and B, then by the definition of betweenness, CA CB = {C}, which is false. Notice that CA  CB = CA. A B C EXAMPLE 1:Show that C is not between A and B.

  6. BA and BC are opposite rays if B is between A and C. Definition

  7. A segment is the set consisting of two points A and B and all the points in between. The symbol for segment AB is AB. AB = {A,B}  {x|A-X-B}. Definition

  8. A point A AB line AB XY half-line XY CD ray CD AC segment AC LM vector LM Symbol Meaning

  9. Example: AB  CB = 1. {B} 2. AC 3. AC 4. AD 5. Both 3 & 4 A B C D

  10. Example: AB  CB = 1. {B} 2. AC 3. AC 4. AD 5. Both 1 & 2 A B C D

  11. Example: AB  CD = 1. { } 2. AD 3. CD 4. CD A B C D

  12. D E A B C Example: 1. Is A between E and B? 1. Yes 2. No

  13. D E A B C Example: 2. Identify a correct betweenness statement 1. A-B-C 2. E-D-C

  14. D E A B C Example: 3. Name four segments.

  15. D E 4. Are CA and AC opposite rays? 1. Yes 2. No A B C Example:

  16. D E A B C Example: 5. Name two pairs of opposite rays.

  17. Homework pp. 46-47

  18. B C F L M K ►A. Exercises Use the figure for exercises 6-12. 9. Name two pairs of opposite rays.

  19. B C F L M K ►A. Exercises Use the figure for exercises 6-12. 11. Name four line segments.

  20. A B C D 13. AB  BC ►B. Exercises Use the figure below and correct notation to describe the set of points in exercises 13-21.

  21. A B C D 15. BC  AC ►B. Exercises Use the figure below and correct notation to describe the set of points in exercises 13-21.

  22. A B C D 17. {A}  AB ►B. Exercises Use the figure below and correct notation to describe the set of points in exercises 13-21.

  23. A B C D 19. DC  AC ►B. Exercises Use the figure below and correct notation to describe the set of points in exercises 13-21.

  24. A B C D ►B. Exercises 21. Name two rays that have B as their endpoint. What is the special name that these two rays have?

  25. 23. What is the intersection of AX and XA? ►B. Exercises

  26. 25. What is the intersection of AB and BA? ►C. Exercises

  27. ■ Cumulative Review Name the postulate that justifies each statement. 26. B is between A and C; therefore BA  {B}  BC = AC

  28. ■ Cumulative Review Name the postulate that justifies each statement. 27. A, B, and C are collinear. B, C, and D are also collinear. Therefore A, C, and D are collinear, and AB = BC = CD.

  29. ■ Cumulative Review Assume that A-B-C and X-B-Y. What kind of lines are AC and XY, if 28. A, X, and B are not collinear.

  30. ■ Cumulative Review Assume that A-B-C and X-B-Y. What kind of lines are AC and XY, if 29. A, X, and B are collinear.

  31. ■ Cumulative Review Assume that A-B-C and X-B-Y. What kind of lines are AC and XY, if 30. Suppose B is between A and C and C is between B and D. Draw two conclusions (include a sketch).

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