3 1, 3-2 parallel lines & transversals

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3 1, 3-2 parallel lines & transversals

  1. 1. PARALLEL LINES, TRANSVERSALS AND SPECIAL ANGLES Jim Smith JCHS Section 3-1, 3-2
  2. 2. A Line That Intersects 2 Or More Lines At Different Points Is Called A Transversal transversal
  3. 3. When This Happens, 8 Angles Are Formed 1 2 3 4 5 6 7 8
  4. 4. This Forms 2 Neighborhoods 1 2 3 4 5 6 7 8
  5. 5. 1 2 3 4 5 6 7 8 Remember Vertical And Linear Angles Vertical
  6. 6. Linear Pairs 1 2 3 4 5 6 7 8
  7. 7. These Angles Are Called Consecutive Or Same Side Angles 1 3 5 7 2 4 6 8
  8. 8. Interior Angles (Between 2 lines) Exterior Angles ( outside the lines) 3 4 5 6 1 2 7 8
  9. 9. Alternate Angles Are On Different Sides Of The Transversal And From Different Neighborhoods 1 2 3 4 5 6 7 8 Alternate Exterior Angles 1 And 8 Angles 2 And 7 Alternate Interior Angles 3 And 6 Angles 4 And 5
  10. 10. 1 3 5 7 2 4 6 8 Consecutive Int Angles 3 and 5 Angles 4 and 6 Consecutive Ext Angles 1 and 7 Angles 2 and 8
  11. 11. 1 2 3 4 5 6 7 8 Corresponding Angles Are Located In The Same Position In Each Neighborhood
  12. 12. Name The Angles <ul><li>11 and 15 </li></ul><ul><li>12 and 16 </li></ul><ul><li>13 and 16 </li></ul><ul><li>12 and 18 </li></ul><ul><li>14 and 16 </li></ul><ul><li>14 and 18 </li></ul><ul><li>11 and 14 </li></ul><ul><li>15 and 17 </li></ul>11 12 13 14 15 16 17 18
  13. 13. <ul><li>Corresponding </li></ul><ul><li>Corresponding </li></ul><ul><li>Alt Interior </li></ul><ul><li>Consecutive (SS) Exterior </li></ul><ul><li>Consecutive (SS) Interior </li></ul><ul><li>Corresponding </li></ul><ul><li>Vertical </li></ul><ul><li>Linear </li></ul>Check Your Answers
  14. 14. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 With This Diagram, We Can Work With Angles In Different Neighborhoods As Long As They Are Connected By A Transversal <ul><li>Name the angles </li></ul><ul><li>1 and 3 </li></ul><ul><li>7 and 12 </li></ul><ul><li>11 and 14 </li></ul><ul><li>6 and 10 </li></ul><ul><li>13 and 5 </li></ul><ul><li>9 and 6 </li></ul><ul><li>1 and 13 </li></ul><ul><li>5 and 4 </li></ul><ul><li>7 and 11 </li></ul><ul><li>6 and 11 </li></ul>
  15. 15. Check Your Answers <ul><li>Corresponding </li></ul><ul><li>Alt. Int. </li></ul><ul><li>Alt. Int. </li></ul><ul><li>Cons. (SS) Int. </li></ul><ul><li>Corresponding </li></ul><ul><li>Alt. Int. </li></ul><ul><li>Consecutive Ext </li></ul><ul><li>Alt. Ext </li></ul><ul><li>Cons. (SS) Int. </li></ul><ul><li>None </li></ul>
  16. 16. Parallel lines Lines that are coplanar and do not intersect
  17. 17. If 2 Parallel Lines Are Cut By A Transversal Then: Corresponding Angles Are Congruent Alternate Interior Angles Are Congruent Same Side Interior Angles Are Supplementary
  18. 18. Remember ……… Even Without Parallel Lines Vertical Angles Are Always Congruent Linear Pairs Are Always Supplementary
  19. 19. m 1 = 105 <ul><li>Find: </li></ul><ul><li>3 = </li></ul><ul><li>6 = </li></ul><ul><li>7 = </li></ul><ul><li>4 = </li></ul><ul><li>5 = </li></ul>75 75 75 105 105 1 2 3 4 5 6 7 8 a b a b
  20. 20. 1 2 3 4 5 6 7 8 a b 63° 117° 119° 119° 119° 119° 61° 63° 63°
  21. 21. 2x+6 3x-10 5x-20 2x-10 2x+6 = 3x-10 6 = x – 10 16 = x 5x-20+2x-10 = 180 7x-30 = 180 7x = 210 x = 30 4x+25 6x-15 4x+25 = 6x-15 25 = 2x-15 40 = 2x 20 = x a b

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