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Parallel Lines and Transversals

Parallel Lines and Transversals. Geometry D – Section 3.1. Parallel Lines and Transversals. What would you call two lines which do not intersect?. Parallel. A solid arrow placed on two lines of a diagram indicate the lines are parallel. The symbol || is used to indicate parallel lines.

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Parallel Lines and Transversals

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  1. Parallel Lines and Transversals Geometry D – Section 3.1

  2. Parallel Lines and Transversals What would you call two lines which do not intersect? Parallel A solid arrow placed on two lines of a diagram indicate the lines are parallel. The symbol || is used to indicate parallel lines. AB || CD

  3. Parallel Lines and Transversals A slash through the parallel symbol || indicates the lines are not parallel. AB || CD

  4. Parallel Lines and Transversals Skew Lines – Two lines are skew if they are not in the same plane and do not intersect. AB does not intersect CD . Since the lines are not in the same plane, they are skew lines.

  5. Parallel Lines and Transversals For the rectangular box shown below, find • All planes parallel to plane CDE.

  6. Parallel Lines and Transversals For the rectangular box shown below, find • All planes parallel to plane CDE. Plane BAH (or any plane with BAHG).

  7. Parallel Lines and Transversals For the rectangular box shown below, find • The intersection of plane AHE and plane CFE.

  8. Parallel Lines and Transversals For the rectangular box shown below, find • The intersection of plane AHE and plane CFE.

  9. Parallel Lines and Transversals For the rectangular box shown below, find • All segments parallel to CD.

  10. Parallel Lines and Transversals For the rectangular box shown below, find • All segments parallel to CD. AB, GH, EF

  11. Parallel Lines and Transversals For the rectangular box shown below, find • All segments that intersect CF.

  12. Parallel Lines and Transversals For the rectangular box shown below, find • All segments that intersect CF.

  13. Parallel Lines and Transversals For the rectangular box shown below, find • All lines skew to GF.

  14. Parallel Lines and Transversals For the rectangular box shown below, find • All lines skew to GF. Segments HE, AD, and BC are || or in the same plane. Segments GH, EF, BG and CF intersect and are in the same plane. These segments are not skew to GF.

  15. Parallel Lines and Transversals Transversal - A transversal is a line which intersects two or more lines in a plane. The intersected lines do not have to be parallel. Lines j, k, and m are intersected by line t. Therefore, line t is a transversal of lines j, k, and m.

  16. Parallel Lines and Transversals Identifying Angles - Exterior angles are on the exterior of the two lines cut by the transversal. 1 3 5 7 2 4 6 8 The exterior angles are:

  17. Parallel Lines and Transversals Identifying Angles - Interior angles are on the interior of the two lines cut by the transversal. 1 3 5 7 2 4 6 8 The interior angles are:

  18. Parallel Lines and Transversals Identifying Angles - Consecutive interior angles are on the interior of the two lines and on the same side of the transversal. 1 3 5 7 2 4 6 8 Consecutive interior angles are:

  19. Parallel Lines and Transversals Identifying Angles - Alternate interior angles are on the interior of the two lines and on opposite sides of the transversal. 1 3 5 7 2 4 6 8 Alternate interior angles are:

  20. Parallel Lines and Transversals Identifying Angles - Alternate exterior angles are on the exterior of the two lines and on opposite sides of the transversal. 1 3 5 7 2 4 6 8 Alternate exterior angles are:

  21. Parallel Lines and Transversals Identifying Angles - Consecutive interior angles are on the interior of the two lines and on the same side of the transversal. 1 3 5 7 2 4 6 8 Consecutive interior angles are:

  22. Parallel Lines and Transversals Identifying Angles - Corresponding angles are on the corresponding side of the two lines and on the same side of the transversal. 1 3 5 7 2 4 6 8 Corresponding angles are:

  23. Parallel Lines and Transversals Identifying Angles – Check for Understanding Determine if the statement is true or false. If false, correct the statement. 1. Line r is a transversal of lines p and q. True – Line r intersects both lines in a plane. 4 3 2 1 5 6 8 7 2. 2 and 10 are alternate interior angles. 9 10 False - The angles are corresponding angles on transversal p. 11 12 15 16 14 13

  24. Parallel Lines and Transversals Identifying Angles – Check for Understanding Determine if the statement is true or false. If false, correct the statement. 3. 3 and 5 are alternate interior angles. False – The angles are vertical angles created by the intersection of q and r. 4 3 2 1 5 6 8 7 4. 1 and 15 are alternate exterior angles. 9 10 11 12 15 16 14 13 True - The angles are alternate exterior angles on transversal p.

  25. Parallel Lines and Transversals Identifying Angles – Check for Understanding Determine if the statement is true or false. If false, correct the statement. 5. 6 and 12 are alternate interior angles. True – The angles are alternate interior angles on transversal q. 4 3 2 1 5 6 8 7 6. 10 and 11 are consecutive interior angles. 9 10 11 12 15 16 14 13 True – The angles are consecutive interior angles on transversal s.

  26. Parallel Lines and Transversals Identifying Angles – Check for Understanding Determine if the statement is true or false. If false, correct the statement. 7. 3 and 4 are alternate exterior angles. False – The angles are a linear pair with linear rays on line r. 4 3 2 1 5 6 8 7 8. 16 and 14 are corresponding angles. 9 10 11 12 15 16 14 13 True – The angles are corresponding on transversal s.

  27. Parallel Lines and Transversals Assignment 3.1 - 16, 20, 24, 26, 28-33, 34-44 even, 47, 51, 54, 59, 60 Reassessment Problems 2.1 / 15 - 27 odd 2.2 / 22, 25, 28, 31, 34, 37, 40, 43, 46, 49 2.3 / 15-21 odd, 22-32 even 2.4 / 13-29 odd 2.5 / 15-33 odd 2.6 / 16, 19, 22, 25, 28, 31, 34

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