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Understanding Relationships Between Lines and Planes in Geometry

This homework assignment focuses on identifying relationships between various lines and planes. In Part I, students will determine which pairs of lines are parallel, perpendicular, or neither. Part II involves a similar analysis with planes. Students will use diagrams to classify lines and planes based on their properties. The keywords include crucial geometric terms such as parallel lines and perpendicular planes. Comprehensive vocabulary definitions are provided to aid understanding. This exercise reinforces critical concepts in geometry necessary for further study.

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Understanding Relationships Between Lines and Planes in Geometry

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  1. Homework: Part I Identify two lines that have the given relationship. 1. parallel lines 2. perpendicular lines 3. neither perpendicular nor parallel

  2. Homework: Part II Identify two planes that appear to have the given relationship. 4. parallel planes 5. perpendicular planes 6. neither perpendicular nor parallel

  3. QP, PQ, QP, QR QR PQ Warm Up Use the diagram to name each figure. P Q R P, Q, R 1. three points 2. a line plane PQR 3. a plane 4. three rays 5. two segments

  4. Vocabulary parallel lines perpendicular lines skew lines parallel planes perpendicular planes

  5. WX || YZ. Parallel lines are lines in the same plane that never intersect. Line WX is parallel to line YZ.

  6. Reading Math The red arrows on lines WX and YZ show that the lines are parallel.

  7. RS | TU. __ Perpendicular lines intersect to form 90o angles, or right angles. Line RS is perpendicular to line TU.

  8. AB and ML are skew. Skew lines are lines that lie in different planes. They are neither parallel nor intersecting. Line AB and line ML are skew lines.

  9. B D C AB || DC Additional Example 1: Identifying Lines in Space Identify two lines that have the given relationship. A. parallel lines A The lines are in the same plane and do not intersect. E

  10. B D C CD | CE __ Additional Example 1: Identifying Lines in Space Identify two lines that have the given relationship. B. perpendicular lines A The lines intersect to form 90o angles. E

  11. 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.

  12. B D C A E AD and CE 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.

  13. NP PS Check It Out! Example 1 Identify two lines that have the given relationship. A. perpendicular lines The lines insect to form 90o angles.

  14. NP and QR 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.

  15. NR and PS 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.

  16. Additional Example 2: Identifying Planes in Space Identify two planes that appear to have the given relationship. A. perpendicular planes K N The planes intersect to form right angles. L J M P plane MPL  plane NPL

  17. Remember! A plane may be named by any three points that are not on the same line.

  18. Additional Example 2: Identifying Planes in Space Identify two planes that appear to have the given relationship. B. parallel planes K N The planes do not intersect. L J plane JKL || plane MNP. M P

  19. 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 angles. N L J plane JMN and plane MPL. M P

  20. Check It Out! Example 2 Identify two planes that appear to have the given relationship. A. perpendicular planes D The planes intersect to form right angles. B plane BAC  plane EAC E F A C

  21. Check It Out! Example 2 Identify two planes that appear to have the given relationship. B. parallel planes D B The planes do not intersect. plane BAC || plane DEF E F A C

  22. 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 do not form right angles. B plane AEF and plane BDF E F A C

  23. FE and DH FK KJ FK || EJ Lesson Quiz: Part I Identify two lines that have the given relationship. 1. parallel lines 2. perpendicular lines 3. neither perpendicular nor parallel

  24. 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

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