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3-1 Parallel Lines and Transversals

3-1 Parallel Lines and Transversals. Page 173. You used angle and line segment relationships to prove theorems. Identify relationships between two lines or two planes. Name angle pairs formed by parallel lines and transversals. Page 173. 8. 6. 4. 2. 6. 8. -2. -8. -6. -4. 2. 4. -2.

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3-1 Parallel Lines and Transversals

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  1. 3-1 Parallel Lines and Transversals Page 173

  2. You used angle and line segment relationships to prove theorems. • Identify relationships between two lines or two planes. • Name angle pairs formed by parallel lines and transversals.

  3. Page 173

  4. 8 6 4 2 6 8 -2 -8 -6 -4 2 4 -2 -4 -6 -8 Parallel Lines Parallel lines are lines in the same plane that never intersect. Parallel lines have the same slope.

  5. Example 1 Determine whether these lines are parallel. y = 4x + 2 y = 4x -6 and The slope of both lines is 4. So, the lines are parallel.

  6. Skew Lines Skew lines are lines that do not intersect and are not coplanar. n A m B

  7. B. Name a segment skew to EH. Answer:AB, CD, BG, or CF

  8. Parallel Planes Parallel planes are planes that do not intersect. A B

  9. C. Name a plane parallel to plane ABG. Answer: plane CDE

  10. Page 174

  11. Transversal Definition A transversal is a line that intersects two coplanar lines at two different points. Transversal t Exterior 1 2 4 3 r Interior 5 6 s 8 7 Exterior

  12. Angles formed by Transversals 1 2 4 3 interior 5 6 8 7 Consecutive interiorangles

  13. Angles formed by Transversals 1 2 4 3 interior 5 6 8 7 Alternateinteriorangles

  14. exterior 4 3 5 6 exterior Angles formed by Transversals 1 2 8 7 Alternateexteriorangles

  15. Angles formed by Transversals 1 2 4 3 5 6 8 7 Correspondingangles

  16. Classify Angle Pair Relationships A. Classify the relationship between 2 and 6 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: corresponding

  17. B. Classify the relationship between 1 and 7 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: alternate exterior

  18. C. Classify the relationship between 3 and 8 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: consecutive interior

  19. D. Classify the relationship between 3 and 5 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: alternate interior

  20. A. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 1 and 2. Then classify the relationship between the pair of angles. Answer: The transversal connecting 1 and 2 is line v. These are corresponding angles.

  21. B. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 2 and 3. Then classify the relationship between the pair of angles. Answer: The transversal connecting 2 and 3 is line v. These are alternate interior angles.

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