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Understanding Lines and Angles: Visual Examples and Notations

Explore parallel, perpendicular lines, transversals, and various angle types with clear illustrations and key facts. Discover how to find missing angle measures using different angle relationships.

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Understanding Lines and Angles: Visual Examples and Notations

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  1. CHAPTER 3 LINES AND ANGLES Free powerpoints at http://www.worldofteaching.com

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

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

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

  5. 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

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

  7. 30 Transversal • Def: a line that intersects two lines at different points • Illustration: t p. 131

  8. 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

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

  10. 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

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

  12. 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

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

  14. 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

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

  16. 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

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

  18. 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

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

  20. HW P. 132 – 133 • # 6 – 9 • # 21 – 26 P. 146 - 147 • #7 - 17

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