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Geometry Notes

Geometry Notes. Lesson 3.1 Lines Cut By A Transversal. Lesson 3-1. Transversal – A line that intersects two or more coplanar lines at different points  Skew lines- lines that do not intersect and are not coplanar. Example 1-1a. Name all planes that are parallel to plane AEF.

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Geometry Notes

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  1. Geometry Notes Lesson 3.1 Lines Cut By A Transversal

  2. Lesson 3-1 • Transversal – A line that intersects two or more coplanar lines at different points  • Skew lines- lines that do not intersect and are not coplanar.

  3. Example 1-1a Name all planes that are parallel to plane AEF. Answer: plane BHG

  4. Name all segments that intersect Answer: Example 1-1b

  5. Name all segments that are parallel to Answer: Example 1-1c

  6. Name all segments that are skew to Answer: Example 1-1d

  7. a. Name all planes that are parallel to plane RST. b. Answer: c. Answer: d. Answer: Example 1-1e Use the figure to name each of the following. Answer: plane XYZ

  8. Example 1-2a BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line v is a transversal. Answer: If the lines are extended, line v intersects lines u, w, x, and z.

  9. Example 1-2b BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line yis a transversal. Answer: lines u, w, x, z

  10. Example 1-2c BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line uis a transversal. Answer: lines v, x, y, z

  11. Example 1-2d BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line wis a transversal. Answer: lines v, x, y, z

  12. a. line a b. line b c. line c d. line d Example 1-2e HIKING A group of nature trails is shown. Identify the sets of lines to which each given line is a transversal. Answer: lines c, d, e, f Answer: lines c, d, e, f Answer: lines a, b, d, e, f Answer: lines a, b, c, e, f

  13. Vocabulary • Vertical Angles – non-adjacent, non-overlapping congruent angles formed by two intersecting lines . (They share a common vertex.) • Linear Pairs of Angles –two adjacent angles whose non-shared rays form a straight angle • Corresponding Angles – angles that lie on the same side of the transversal and in corresponding positions relative to the parallel lines

  14. Vocabulary • Alternate Interior Angles – nonadjacent angles between the parallel lines that lie on opposite sides of the transversal • Alternate Exterior Angles – nonadjacent angles outside the parallel lines that lie on opposite sides of the transversal • Same-Side Interior Angles – angles that lie on the same side of the transversal and between the parallel lines

  15. Identify as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Example 1-3a Answer: corresponding

  16. Identify as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Example 1-3b Answer: alternate exterior

  17. Identify as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Example 1-3c Answer: corresponding

  18. Identify as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Example 1-3d Answer: alternate exterior

  19. Identify as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Example 1-3e Answer: alternate interior

  20. Identify as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Example 1-3f Answer: consecutive interior

  21. a. b. c. Example 1-3g Identify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: consecutive interior Answer: corresponding Answer: alternate exterior

  22. d. e. f. Example 1-3g Identify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: alternate interior Answer: corresponding Answer: alternate exterior

  23. Homework 10/6 • Lesson 3-1 p.126 #22-47 (25probs)

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