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3 1, 3-2 parallel lines & transversals
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3 1, 3-2 parallel lines & transversals

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  • 1. PARALLEL LINES, TRANSVERSALS AND SPECIAL ANGLES Jim Smith JCHS Section 3-1, 3-2
  • 2. A Line That Intersects 2 Or More Lines At Different Points Is Called A Transversal transversal
  • 3. When This Happens, 8 Angles Are Formed 1 2 3 4 5 6 7 8
  • 4. This Forms 2 Neighborhoods 1 2 3 4 5 6 7 8
  • 5. 1 2 3 4 5 6 7 8 Remember Vertical And Linear Angles Vertical
  • 6. Linear Pairs 1 2 3 4 5 6 7 8
  • 7. These Angles Are Called Consecutive Or Same Side Angles 1 3 5 7 2 4 6 8
  • 8. Interior Angles (Between 2 lines) Exterior Angles ( outside the lines) 3 4 5 6 1 2 7 8
  • 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. 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. 1 2 3 4 5 6 7 8 Corresponding Angles Are Located In The Same Position In Each Neighborhood
  • 12. Name The Angles
    • 11 and 15
    • 12 and 16
    • 13 and 16
    • 12 and 18
    • 14 and 16
    • 14 and 18
    • 11 and 14
    • 15 and 17
    11 12 13 14 15 16 17 18
  • 13.
    • Corresponding
    • Corresponding
    • Alt Interior
    • Consecutive (SS) Exterior
    • Consecutive (SS) Interior
    • Corresponding
    • Vertical
    • Linear
    Check Your Answers
  • 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
    • Name the angles
    • 1 and 3
    • 7 and 12
    • 11 and 14
    • 6 and 10
    • 13 and 5
    • 9 and 6
    • 1 and 13
    • 5 and 4
    • 7 and 11
    • 6 and 11
  • 15. Check Your Answers
    • Corresponding
    • Alt. Int.
    • Alt. Int.
    • Cons. (SS) Int.
    • Corresponding
    • Alt. Int.
    • Consecutive Ext
    • Alt. Ext
    • Cons. (SS) Int.
    • None
  • 16. Parallel lines Lines that are coplanar and do not intersect
  • 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. Remember ……… Even Without Parallel Lines Vertical Angles Are Always Congruent Linear Pairs Are Always Supplementary
  • 19. m 1 = 105
    • Find:
    • 3 =
    • 6 =
    • 7 =
    • 4 =
    • 5 =
    75 75 75 105 105 1 2 3 4 5 6 7 8 a b a b
  • 20. 1 2 3 4 5 6 7 8 a b 63° 117° 119° 119° 119° 119° 61° 63° 63°
  • 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