8-2 Geometric Relationships Common Core State Standards Learning Objective 7.G.5 Solve for an unknown angle using the “properties of angles.” Holt CA Course 1 8-2 Geometric Relationships Vocabulary parallel lines perpendicular lines skew lines parallel planes perpendicular planes 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. Holt CA Course 1 8-2 Geometric Relationships Reading Math The red arrows on lines WX and YZ show that the lines are parallel. Holt CA Course 1 8-2 Geometric Relationships Perpendicular lines intersect to form 90o angles, or right angles. Line RS is perpendicular to line TU. RS __ | TU. 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. Holt CA Course 1 8-2 Geometric Relationships Additional Example 1: Identifying Lines in Space Identify two lines that have the given relationship. A. parallel lines The lines are in the same plane and do not intersect. AB || DC Holt CA Course 1 A D B C E 8-2 Geometric Relationships Additional Example 1: Identifying Lines in Space Identify two lines that have the given relationship. B. perpendicular lines The lines intersect to form 90o angles. CD __ | CE Holt CA Course 1 A D B C E 8-2 Geometric Relationships Caution! 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. Holt CA Course 1 8-2 Geometric Relationships Additional Example 1: Identifying Lines in Space Identify two lines that have the given relationship. C. skew lines The lines lie in different planes. They are neither parallel nor intersecting. AD and CE Holt CA Course 1 A D B C E 8-2 Geometric Relationships Check It Out! Example 1 Identify two lines that have the given relationship. A. perpendicular lines The lines insect to form 90o angles. NP PS Holt CA Course 1 8-2 Geometric Relationships Check It Out! Example 1 Identify two lines that have the given relationship. B. skew lines The lines lie in different planes. They are neither parallel nor intersecting. NP and QR Holt CA Course 1 8-2 Geometric Relationships Check It Out! Example 1 Identify two lines that have the given relationship. C. parallel lines The lines are in the same plane and do not intersect. NR and PS Holt CA Course 1 8-2 Geometric Relationships Holt CA Course 1 8-2 Geometric Relationships Additional Example 2: Identifying Planes in Space Identify two planes that appear to have the given relationship. K A. perpendicular planes The planes intersect to form right angles. plane MPL plane NPL Holt CA Course 1 N L J M P 8-2 Geometric Relationships Remember! A plane may be named by any three points that are not on the same line. Holt CA Course 1 8-2 Geometric Relationships Additional Example 2: Identifying Planes in Space Identify two planes that appear to have the given relationship. K B. parallel planes The planes do not intersect. plane JKL || plane MNP. Holt CA Course 1 N L J M P 8-2 Geometric Relationships Additional Example 2: Identifying Planes in Space Identify two planes that appear to have the given relationship. C. neither perpendicular nor parallel planes K The planes intersect, but they do not form right L J angles. plane JMN and plane MPL. Holt CA Course 1 M N P 8-2 Geometric Relationships Check It Out! Example 2 Identify two planes that appear to have the given relationship. D A. perpendicular planes The planes intersect to form right angles. B plane BAC plane EAC E A Holt CA Course 1 F C 8-2 Geometric Relationships Check It Out! Example 2 Identify two planes that appear to have the given relationship. D B. parallel planes B The planes do not intersect. plane BAC || plane DEF E A Holt CA Course 1 F C 8-2 Geometric Relationships Check It Out! Example 2 Identify two planes that appear to have the given relationship. C. neither perpendicular nor parallel planes D The planes intersect, but they B do not form right angles. plane AEF and plane BDF E A Holt CA Course 1 F C 8-2 Geometric Relationships Lesson Quiz: Part I Identify two lines that have the given relationship. 1. parallel lines FK || EJ 2. perpendicular lines FK KJ 3. neither perpendicular nor parallel FE and DH 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 plane SPQ || plane WTU 5. perpendicular planes plane PSW plane WSR 6. neither perpendicular nor parallel plane PQU and plane RQU Holt CA Course 1 8-2 Geometric Relationships Classwork & Homework Lesson 8-2 Practice B Lesson 8-2 Problem Solving Holt CA Course 1

1/--страниц