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Geometry Notes

This lesson covers key concepts related to lines and transversals in geometry. A transversal is defined as a line that intersects two or more coplanar lines at different points. The lesson explores various types of lines, including skew lines that do not intersect and are not coplanar. Students will learn to identify parallel lines, segments, and angles formed by transversals, including vertical angles, linear pairs, corresponding angles, and alternate interior and exterior angles. Various examples and exercises help reinforce understanding.

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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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