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3-1 Parallel Lines and Transversals

3-1 Parallel Lines and Transversals. CCSS. Content Standards G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Mathematical Practices

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3-1 Parallel Lines and Transversals

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  1. 3-1 Parallel Lines and Transversals

  2. CCSS Content Standards G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others.

  3. Then/Now 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.

  4. Vocabulary • parallel lines • skew lines • parallel planes • transversal • interior angles • exterior angles • consecutive interior angles • alternate interior angles • alternate exterior angles • corresponding angles

  5. Concept

  6. Vocabulary • transversal: • a line that intersects two or more coplanar lines at two different points

  7. A. Name all segments parallel to BC. Answer:AD, EH, FG Example 1

  8. B. Name a segment skew to EH. Answer:AB, CD, BG, or CF Example 1

  9. Example 1 C. Name a plane parallel to plane ABG. Answer: plane CDE

  10. Example 1a A. Name a plane that is parallel to plane RST. A. plane WTZ B. plane SYZ C. plane WXY D. plane QRX

  11. B. Name a segment that intersects YZ. A.XY B.WX C.QW D.RS Example 1b

  12. C. Name a segment that is parallel to RX. A.ZW B.TZ C.QR D.ST Example 1c

  13. Concept

  14. Vocabulary • Interior angles • Example:

  15. Vocabulary • Exterior angles • Example:

  16. Vocabulary • Consecutive interior angles • Example:

  17. Vocabulary • Alternate interior angles • Example:

  18. Vocabulary • Alternate exterior angles • Example:

  19. Vocabulary • Corresponding angles • Example:

  20. Example 2 A. Classify the relationship between 2 and 6 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: corresponding

  21. Example 2 B. Classify the relationship between 1 and 7 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: alternate exterior

  22. Example 2 C. Classify the relationship between 3 and 8 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: consecutive interior

  23. Example 2 D. Classify the relationship between 3 and 5 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: alternate interior

  24. Example 2a A. Classify the relationship between 4 and 5. A. alternate interior B. alternate exterior C. corresponding D. consecutive interior

  25. Example 2b B. Classify the relationship between 7 and 9. A. alternate interior B. alternate exterior C. corresponding D. consecutive interior

  26. Example 2c C. Classify the relationship between 4 and 7. A. alternate interior B. alternate exterior C. corresponding D. consecutive interior

  27. Example 2d D. Classify the relationship between 2 and 11. A. alternate interior B. alternate exterior C. corresponding D. consecutive interior

  28. Example 3 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.

  29. Example 3 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.

  30. Example 3 C. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 4 and 5. Then classify the relationship between the pair of angles. Answer: The transversal connecting 4 and 5 is line y. These are consecutive interior angles.

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