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  1. 5 6 4 7 8 3 2 t 1 Warm up List all pairs of angles that fit the description. • Corresponding • Alternate Interior • Alternate Exterior • Consecutive Interior

  2. LINES AND ANGLES

  3. B A D l C m 28 PARALLEL LINES • Def: line that do not intersect. • Illustration: • Notation:l || mAB|| CD p. 129

  4. Examples of Parallel Lines • Hardwood Floor • Opposite sides of windows, desks, etc. • Parking slots in parking lot • Parallel Parking • Streets: Laramie & LeClaire

  5. Examples of Parallel Lines • Streets: Belmont & School

  6. m n 29 PERPENDICULAR LINES • Def: Lines that intersect to form a right angle. • Illustration: • Notation:m n • Key Fact: 4 right angles are formed. p. 79

  7. Ex. of Perpendicular Lines • Window panes • Streets: Belmont and Cicero

  8. 30 Transversal • Def: a line that intersects two lines at different points • Illustration: t p. 131

  9. Vertical Angles • Two angles that are opposite angles. t • 14 • 2  3 • 5  8 • 6  7 1 2 4 3 6 5 7 8

  10. Vertical Angles • Find the measures of the missing angles t 125  ? 125  55  ? 55 

  11. t 1 2 4 3 6 5 7 8 Supplementary Angles/Linear Pair • Two angles that form a line (sum=180) • 1+2=180 • 2+4=180 • 4+3=180 • 3+1=180 • 5+6=180 • 6+8=180 • 8+7=180 • 7+5=180

  12. Supplementary Angles/Linear Pair • Find the measures of the missing angles t ? 108  72  180 - 72 ? 108 

  13. 1 2 3 4 5 6 7 8 30 Corresponding Angles • Two angles that occupy corresponding positions. t • 15 • 2  6 • 3  7 • 4  8 Top Left Top Right Bottom Left Bottom Right Top Left Top Right Bottom Left Bottom Right p. 131 & 143

  14. Corresponding Angles • Find the measures of the missing angles t 145  35  ? 145 

  15. 30 Alternate Interior Angles • Two angles that lie between parallel lines on opposite sides of the transversal t • 3  6 • 4  5 1 2 3 4 5 6 7 8 p. 131 & 143

  16. Alternate InteriorAngles • Find the measures of the missing angles t 82  82  98  ?

  17. 30 Alternate Exterior Angles • Two angles that lie outside parallel lines on opposite sides of the transversal t • 2  7 • 1  8 1 2 3 4 5 6 7 8 p. 131 & 143

  18. Alternate ExteriorAngles • Find the measures of the missing angles t 120  ? 120  60 

  19. 30 Consecutive Interior Angles • Two angles that lie between parallel lines on the same sides of the transversal t • 3 +5 = 180 • 4 +6 = 180 1 2 3 4 5 6 7 8 p. 131 & 143

  20. Consecutive InteriorAngles • Find the measures of the missing angles t 180 - 135 135  45  ?

  21. Corresponding 4 and 2 3 and 1 5 and 7 6 and 8 5 6 4 7 8 3 2 t 1

  22. Alternate Interior 3 and 7 2 and 6 5 6 4 7 8 3 2 t 1

  23. Alternate Exterior 5 and 1 4 and 8 5 6 4 7 8 3 2 t 1

  24. Consecutive Interior 5 3 and 2 6 and 7 6 4 7 8 3 2 t 1

  25. Find all angle measures t 180 - 67 113  67  1 3 67  2 113  113  5 67  8 67  6 7 113 

  26. LINES AND ANGLES Part II: Equations

  27. Alternate Exterior Angles • Name the angle relationship • Are they congruent or supplementary? • Find the value of x  t 5x = 125 125  5 5 x = 25 5x 

  28. Corresponding Angles • Name the angle relationship • Are they congruent or supplementary? • Find the value of x  t 2x + 1 = 151 - 1 - 1 2x + 1 2x = 150 2 2 151 x = 75

  29. Consecutive Interior Angles • Name the angle relationship • Are they congruent or supplementary? • Find the value of x supp t 7x + 15 + 81 = 180 7x + 96 = 180 - 96 - 96 81 7x = 84 7x + 15 7 7 x = 12

  30. Alternate Interior Angles • Name the angle relationship • Are they congruent or supplementary? • Find the value of x  t 2x + 20 = 3x - 2x - 2x 3x 20 = x 2x + 20