1. Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc., Cincinnati, Ohio 45202 Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240 3.1 Parallel Lines and Transversals

2. Objectives Identify the relationships between two lines or two planes Name angles formed by a pair of lines and a transversal

3. Relationships Between Lines Parallel Lines – lines that are coplanar and do not intersect; We use the symbol || to represent parallel lines, (i.e. AB || CD). Skew Lines – lines that do not intersect and are not coplanar Parallel Planes – two planes that do not intersect

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

5. Name all segments that intersect Answer: Example 1b:

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

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

8. Use the figure to name each of the following. Answer: plane XYZ a. Name all planes that are parallel to plane RST. b. c. d. Answer: Your Turn:

9. Relationships Between Lines and the Angles Formed Transversal - a line that intersects two or more coplanar lines at different points 2 4 7 1 3 56 8 Angles 1 and 5 are corresponding angles Angles 1 and 8 are alternate exterior angles

10. Relationships Between Lines and the Angles Formed Angles 3 and 6 are alternate interior angles. Angles 3 and 5 are consecutive interior angles or same side interior angles 2 4 7 1 3 56 8

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

12. BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line y is a transversal. Answer: w and u, w and x, w and z, u and z Example 2b:

13. BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line u is a transversal. Answer: v and y, y and x, v and z, y and z Example 2c:

14. BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line w is a transversal. Answer: v and y, y and x, v and z, y and z Example 2d:

15. 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 a, b, d, e, f a. line a b. line b c. line c d. line d Answer: lines a, b, c, e, f Your Turn:

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

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

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

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

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

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

22. Identify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: consecutive interior Answer: corresponding Answer: alternate exterior a. b. c. Your Turn:

23. Identify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: alternate interior Answer: corresponding Answer: alternate exterior d. e. f. Your Turn:

24. Assignment Geometry: Pg. 128 – 130 #2 – 48 evens Pre-AP Geometry: Pg. 128 – 130 #2 – 48 evens, #58