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Warm up

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. LINES AND ANGLES. B. A. D. l. C. m. 28. PARALLEL LINES. Def: line that do not intersect. Illustration:

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Warm up

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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

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