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Bell Work

Learn about parallel lines, transversals, and the different types of angles formed by them. Use given information and reasoning to complete proofs.

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Bell Work

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  1. Bell Work

  2. ________________ PARALLEL LINES, TRANSVERSALS AND SPECIAL ANGLES Section 3-1, 3-2

  3. Use the diagram and the given information to complete the missing steps and reasons in the proof. GIVEN: LK = 5, JK = 5, JK ≅ JL PROVE: LK ≅ JL ________ ________ 3. LK = JK 4. JK ≅ JL 5. __________ Bell work 9-30 • Given • Given • Transitive Property 5. Transitive Property

  4. A Line That Intersects 2 Or More Lines At Different Points Is Called A Transversal transversal

  5. 3 1 5 7 4 2 6 8 When This Happens, 8 Angles Are Formed

  6. 5 1 3 7 4 6 8 2 This Forms 2 Neighborhoods

  7. Remember Vertical And Linear Angles Vertical 3 7 5 1 4 6 8 2

  8. Linear Pairs 3 7 5 1 4 6 8 2

  9. 5 1 3 7 4 6 8 2 These Angles Are Called Consecutive Or Same Side Angles

  10. 5 3 4 6 1 7 8 2 Interior Angles (Between 2 lines) Exterior Angles (outside the lines)

  11. Alternate Angles Are On Different Sides Of The Transversal And From Different Neighborhoods Alternate Exterior Angles 1 And 8 Angles 2 And 7 Alternate Interior Angles 3 And 6 Angles 4 And 5 5 1 3 7 4 6 8 2

  12. Consecutive Int Angles 3 and 5 Angles 4 and 6 5 3 4 6 Consecutive Ext Angles 1 and 7 Angles 2 and 8 1 7 8 2

  13. 3 7 5 1 4 6 8 2 Corresponding Angles Are Located In The Same Position In Each Neighborhood

  14. 12 11 14 13 15 16 17 18 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

  15. Check Your Answers • Corresponding • Corresponding • Alt Interior • Consecutive (SS) Exterior • Consecutive (SS) Interior • Corresponding • Vertical • Linear

  16. 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 4 3 2 1 8 7 6 5 12 11 10 9 16 15 14 13 With This Diagram, We Can Work With Angles In Different Neighborhoods As Long As They Are Connected By A Transversal

  17. Check Your Answers • Corresponding • Alt. Int. • Alt. Int. • Cons. (SS) Int. • Corresponding • Alt. Int. • Consecutive Ext • Alt. Ext • Cons. (SS) Int. • None

  18. Parallel lines Lines that are coplanar and do not intersect

  19. 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

  20. Remember ……… Even Without Parallel Lines Vertical Angles Are Always Congruent Linear Pairs Are Always Supplementary

  21. a b 1 2 a 3 4 6 5 b 8 7 m 1 = 105 • Find: • 3 = • 6 = • 7 = • 4 = • 5 = 75 75 75 105 105

  22. a b 2x+6 4x+25 5x-20 3x-10 2x-10

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