1. Holt CA Course 1 8-2 Geometric Relationships 7.G.5 Solve for an unknown angle using the “properties of angles.” Common Core State Standards Learning Objective

2. Holt CA Course 1 8-2 Geometric Relationships Vocabulary parallel lines perpendicular lines skew lines parallel planes perpendicular planes

3. Holt CA Course 1 8-2 Geometric Relationships Parallel lines are lines in the same plane that never intersect. Line WX is parallel to line YZ. WX || YZ.

4. Holt CA Course 1 8-2 Geometric Relationships The red arrows on lines WX and YZ show that the lines are parallel. Reading Math

5. Holt CA Course 1 8-2 Geometric Relationships Perpendicular lines intersect to form 90 o angles, or right angles. Line RS is perpendicular to line TU. RS | TU. __

6. Holt CA Course 1 8-2 Geometric Relationships Skew lines are lines that lie in different planes. They are neither parallel nor intersecting. Line AB and line ML are skew lines. AB and ML are skew.

7. Holt CA Course 1 8-2 Geometric Relationships Identify two lines that have the given relationship. A. parallel lines Additional Example 1: Identifying Lines in Space The lines are in the same plane and do not intersect. D C BA E AB || DC

8. Holt CA Course 1 8-2 Geometric Relationships Identify two lines that have the given relationship. B. perpendicular lines Additional Example 1: Identifying Lines in Space The lines intersect to form 90 o angles. D C BA E CD | CE __

9. Holt CA Course 1 8-2 Geometric Relationships Two lines may be perpendicular even though they do not appear to be perpendicular. Use the markings on the drawings and read the problem carefully to determine which lines are perpendicular. Caution!

10. Holt CA Course 1 8-2 Geometric Relationships Identify two lines that have the given relationship. C. skew lines Additional Example 1: Identifying Lines in Space The lines lie in different planes. They are neither parallel nor intersecting. D C BA E AD and CE

11. Holt CA Course 1 8-2 Geometric Relationships Check It Out! Example 1 NP  PS Identify two lines that have the given relationship. A. perpendicular lines The lines insect to form 90 o angles.

12. Holt CA Course 1 8-2 Geometric Relationships Check It Out! Example 1 NP and QR Identify two lines that have the given relationship. B. skew lines The lines lie in different planes. They are neither parallel nor intersecting.

13. Holt CA Course 1 8-2 Geometric Relationships Check It Out! Example 1 NR and PS Identify two lines that have the given relationship. C. parallel lines The lines are in the same plane and do not intersect.

14. Holt CA Course 1 8-2 Geometric Relationships

15. Holt CA Course 1 8-2 Geometric Relationships Identify two planes that appear to have the given relationship. A. perpendicular planes Additional Example 2: Identifying Planes in Space The planes intersect to form right angles. M J K N P plane MPL  plane NPL L

16. Holt CA Course 1 8-2 Geometric Relationships A plane may be named by any three points that are not on the same line. Remember!

17. Holt CA Course 1 8-2 Geometric Relationships Identify two planes that appear to have the given relationship. B. parallel planes Additional Example 2: Identifying Planes in Space The planes do not intersect. M J K N P L plane JKL || plane MNP.

18. Holt CA Course 1 8-2 Geometric Relationships Identify two planes that appear to have the given relationship. C. neither perpendicular nor parallel planes Additional Example 2: Identifying Planes in Space The planes intersect, but they do not form right angles. M J K N P L plane JMN and plane MPL.

19. Holt CA Course 1 8-2 Geometric Relationships Identify two planes that appear to have the given relationship. A. perpendicular planes Check It Out! Example 2 The planes intersect to form right angles. plane BAC  plane EAC B D F CA E

20. Holt CA Course 1 8-2 Geometric Relationships Identify two planes that appear to have the given relationship. B. parallel planes Check It Out! Example 2 The planes do not intersect. plane BAC || plane DEF B D F CA E

21. Holt CA Course 1 8-2 Geometric Relationships Identify two planes that appear to have the given relationship. C. neither perpendicular nor parallel planes Check It Out! Example 2 The planes intersect, but they do not form right angles. plane AEF and plane BDF B D F CA E

22. Holt CA Course 1 8-2 Geometric Relationships Lesson Quiz: Part I Identify two lines that have the given relationship. 1. parallel lines 2. perpendicular lines 3. neither perpendicular nor parallel FK || EJ FK  KJ FE and DH

23. Holt CA Course 1 8-2 Geometric Relationships Lesson Quiz: Part II Identify two planes that appear to have the given relationship. 4. parallel planes 5. perpendicular planes 6. neither perpendicular nor parallel plane SPQ || plane WTU plane PSW  plane WSR plane PQU and plane RQU

24. Holt CA Course 1 8-2 Geometric Relationships Classwork & Homework Lesson 8-2 Practice B Lesson 8-2 Problem Solving