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# 3 1, 3-2 parallel lines & transversals

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### Transcript

• 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
• 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
• 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 â€¦â€¦â€¦ 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 63Â° 117Â° 119Â° 119Â° 119Â° 119Â° 61Â° 63Â° 63Â°
• 21. 2x+6 3x-10 5x-20 2x-10 2x+6 = 3x-10 6 = x â€“ 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