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Lines and angles

CHAPTER 6 LINES AND ANGLE CLASS 9

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Lines and angles

  1. 1. CHAPTER LINES AND ANGLES
  2. 2. ∗ Def: line that do not intersect. ∗ Illustration: ∗ Notation: l || m AB || CD PARALLEL LINES l m A B C D 2
  3. 3. Examples of Parallel Lines • Hardwood Floor • Opposite sides of windows, desks, etc. • Parking slots in parking lot • Parallel Parking • Streets: Laramie & LeClaire
  4. 4. Examples of Parallel Lines • Streets: Belmont & School
  5. 5. ∗ Def: Lines that intersect to form a right angle. ∗ Illustration: ∗ Notation: m ⊥ n ∗ Key Fact: 4 right angles are formed. PERPENDICULAR LINES m n 5
  6. 6. Ex. of Perpendicular Lines • Window panes • Streets: Belmont and Cicero
  7. 7. ∗ Def: a line that intersects two lines at different points ∗ Illustration: Transversal t 7
  8. 8. ∗ Two angles that are opposite angles. Vertical Angles 1 2 3 4 5 6 7 8 t ∠1 ≅ ∠ 4 ∠2 ≅ ∠ 3 ∠5 ≅ ∠ 8 ∠6 ≅ ∠ 7
  9. 9. ∗ Find the measures of the missing angles Vertical Angles 125 ° ? ? 55 ° t 55 ° 125 °
  10. 10. ∗ Two angles that form a line (sum=180°) Supplementary Angles/ Linear Pair 1 2 3 4 5 6 7 8 t ∠5+∠6=180 ∠6+∠8=180 ∠8+∠7=180 ∠7+∠5=180 ∠1+∠2=180 ∠2+∠4=180 ∠4+∠3=180 ∠3+∠1=180
  11. 11. ∗ Find the measures of the missing angles Supplementary Angles/ Linear Pair ? 72 ° ? t 108 ° 108 ° 180 - 72
  12. 12. ∗ Two angles that occupy corresponding positions. Corresponding Angles Top Left t Top Left Top Right Top Right Bottom Right Bottom Right Bottom Left Bottom Left ∠1 ≅ ∠ 5 ∠2 ≅ ∠ 6 ∠3 ≅ ∠ 7 ∠4 ≅ ∠ 8 1 2 3 4 5 6 7 8 12
  13. 13. ∗ Find the measures of the missing angles Corresponding Angles 145 ° ? t 35 ° 145 °
  14. 14. ∗ Two angles that lie between parallel lines on opposite sides of the transversal Alternate Interior Angles t ∠3 ≅ ∠ 6 ∠4 ≅ ∠ 5 1 2 3 4 5 6 7 8 14
  15. 15. ∗ Find the measures of the missing angles Alternate Interior Angles 82 ° ? t 98 ° 82 °
  16. 16. ∗ Two angles that lie outside parallel lines on opposite sides of the transversal Alternate Exterior Angles t ∠2 ≅ ∠ 7 ∠1 ≅ ∠ 8 1 2 3 4 5 6 7 8 16
  17. 17. ∗ Find the measures of the missing angles Alternate Exterior Angles 120 ° ? t 60 ° 120 °
  18. 18. ∗ Two angles that lie between parallel lines on the same sides of the transversal Consecutive Interior Angles t ∠3 +∠5 = 180 ∠4 +∠6 = 180 1 2 3 4 5 6 7 8 p. 131 & 143 30
  19. 19. ∗ Find the measures of the missing angles Consecutive Interior Angles ? t 135 ° 45 ° 180 - 135

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