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Angles formed by Transversal and Parallel Lines March 9, 2011

Angles formed by Transversal and Parallel Lines March 9, 2011. Warm Up 3/12/12. Warm Up 3/9/12. q. p. Parallel Lines are…. …..coplanar lines that do not intersect. m. m || n. n. Skew lines are non-coplanar, non-intersecting lines.

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Angles formed by Transversal and Parallel Lines March 9, 2011

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  1. Angles formed by Transversal and Parallel Lines March 9, 2011

  2. Warm Up 3/12/12

  3. Warm Up 3/9/12

  4. q p Parallel Lines are… …..coplanar lines that do not intersect. m m || n n Skew lines are non-coplanar, non-intersecting lines.

  5. Any line that intersects two or more coplanar lines. t r s The Transversal

  6. When lines intersect, angles are formed in several locations. t r s The Transversal

  7. Determine the two sets of angles that are congruent. 1, 4, 5, 8 2, 3, 6, 7 t r 1 2 3 4 5 6 s 8 7 When parallel lines are cut by a transversal…

  8. Angle pair relationships are formed. Some angle pairs are congruent and other angle pairs are supplementary. t r 1 2 3 4 5 6 s 8 7 When parallel lines are cut by a transversal…

  9. Congruent angles have the same measure. t r 1 2 3 4 5 6 s 8 7 When parallel lines are cut by a transversal…

  10. SupplementaryAngles are angles that have a sum of 180 degrees. t r 1 2 3 4 5 6 s 8 7 When parallel lines are cut by a transversal…

  11. Certain angles are given "names" that describe "where" the angles are located in relation to the lines. t r 1 2 3 4 5 6 s 8 7 When parallel lines are cut by a transversal…

  12. t r 1 2 3 4 5 6 s 8 7 When parallel lines are cut by a transversal… INTERIOR

  13. t r 1 2 3 4 5 6 s 8 7 When parallel lines are cut by a transversal… EXTERIOR EXTERIOR

  14. Corresponding angles are congruent angles on the same side of the transversal. t r 1 5 s Corresponding Angles

  15. . t r 2 6 s Corresponding Angles

  16. t r 3 s 7 Corresponding Angles

  17. t r 4 s 8 Corresponding Angles

  18. Alternate Interior angles are congruent angles on opposite sides of the transversal and inside the parallel lines. t r 3 6 s Alternate Interior Angles

  19. t r 4 5 s Alternate Interior Angles

  20. Alternate Exterior angles are congruent angles on opposite sides of the transversal and outside the parallel lines. t r 2 s 7 Alternate Exterior Angles

  21. t r 1 s 8 Alternate Exterior Angles

  22. Same side interior angles are supplementary angles on the same side of the transversal and inside the parallel lines. t r 4 6 s Same Side Interior

  23. t r 3 5 s Same Side Interior

  24. Same side exterior angles are supplementary angles on the same side of the transversal and outside the parallel lines. t r 2 s 8 Same Side Exterior

  25. t r 1 s 7 Same Side Exterior

  26. t r 1 2 4 3 5 6 s 7 8 Vertical Angles Vertical angles are congruent angles located diagonally opposite each other.

  27. t r 2 3 s Vertical Angles

  28. t r 5 s 8 Vertical Angles

  29. t r 6 s 7 Vertical Angles

  30. Angle 2 measures 110°. What other angles have the same measure? 1. 2. 3. 4. 5. 6. 7. 8.

  31. Answer: 1. 2. 3. 4. 5. 6. 7. 8.

  32. What is the measure of ? 1. 2. 3. 4. 5. 6. 7. 8.

  33. What is the measure of ? Answer: 1. 2. 3. 4. 5. 6. 7. 8.

  34. 9) Lines l and m are parallel.l||mFind the missing angles. 42° 2 3 4 l 5 6 7 8 m

  35. 9) Lines l and m are parallel.l||mFind the missing angles. 42° 138° 138° 42° l 42° 138° 138° 42° m

  36. 10) Lines l and m are parallel.l||mFind the missing angles. 81° 2 3 4 l 5 6 7 8 m

  37. 10) Lines l and m are parallel.l||mFind the missing angles. 81° 99° 99° 81° l 81° 99° 99° 81° m

  38. In the diagram below, j ║ k. What is m 1? k j 1 120°

  39. m 1 + 120° = 180° m 1 = 60° Solution

  40. Find the value for x 125° 4 (x + 15)°

  41. m4 = 125° m4 +(x+15)°=180° 125°+(x+15)°= 180° x = 40 Solution

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