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LINE AND ANGLE RELATIONSHIPS Free powerpoints at  http:// www.worldofteaching.com
TYPES OF ANGLES <ul><li>Acute Angles have measures less than 90°. </li></ul><ul><li>Right Angles have measures equal to 90...
PARALLEL LINES <ul><li>Def:  Lines that do not intersect.  Parallel lines are always the same distance apart. </li></ul><u...
PERPENDICULAR LINES <ul><li>Def:  Lines that intersect to form a right angle. </li></ul><ul><li>Illustration: </li></ul><u...
<ul><li>Def:  A line that intersects two lines at different points. </li></ul><ul><li>Illustration: </li></ul>Transversal t
Vertical Angles <ul><li>Two angles that are opposite angles. </li></ul>1 2 3 4 5 6 7 8 t <ul><li>1         4 </li></ul><...
Vertical Angles <ul><li>Find the measures of the missing angles </li></ul>125     ? ? 55     t
Vertical Angles <ul><li>Find the measures of the missing angles </li></ul>125     55     t 55     125  
Angle Relationships <ul><li>Complementary Angles are two angles whose sum is 90°. </li></ul><ul><li>Supplementary Angles a...
Supplementary Angles/ Linear Pair <ul><li>Two angles that form a  line  (sum=180  )  </li></ul><ul><li>5+  6=180 </li></...
Supplementary Angles/ Linear Pair <ul><li>Find the measures of the missing angles </li></ul>? 72   ? t 180 - 72
Supplementary Angles/ Linear Pair <ul><li>Find the measures of the missing angles </li></ul>72   t 108   108   180 - 72
Corresponding Angles <ul><li>Two angles that occupy corresponding positions. </li></ul>Top Left t Top Left Top Right Top R...
Corresponding Angles <ul><li>Find the measures of the missing angles </li></ul>145     ? t 35  
Corresponding Angles <ul><li>Find the measures of the missing angles </li></ul>145     t 35     145  
Alternate Interior Angles <ul><li>Two angles that lie between parallel lines on opposite sides of the transversal </li></u...
Alternate Interior Angles <ul><li>Find the measures of the missing angles </li></ul>82     ? t 98  
Alternate Interior Angles <ul><li>Find the measures of the missing angles </li></ul>82     t 98     82  
Alternate Exterior Angles <ul><li>Two angles that lie outside parallel lines on opposite sides of the transversal </li></u...
Alternate Exterior Angles <ul><li>Find the measures of the missing angles </li></ul>120     ? t 60  
Alternate Exterior Angles <ul><li>Find the measures of the missing angles </li></ul>120     t 60     120  
Consecutive Interior Angles <ul><li>Two angles that lie between parallel lines on the same sides of the transversal </li><...
Consecutive Interior Angles <ul><li>Find the measures of the missing angles </li></ul>? t 135     180 - 135
Consecutive Interior Angles <ul><li>Find the measures of the missing angles </li></ul>t 135     45     180 - 135
This presentation is a modified version of the Slideshow: “ Lines and Angles 2 ” by Miss Patel.  The original Slideshow Pr...
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Line And Angle Relationships

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Line And Angle Relationships

  1. 1. LINE AND ANGLE RELATIONSHIPS Free powerpoints at http:// www.worldofteaching.com
  2. 2. TYPES OF ANGLES <ul><li>Acute Angles have measures less than 90°. </li></ul><ul><li>Right Angles have measures equal to 90°. </li></ul><ul><li>Obtuse Angles have measures between 90° and 180°. </li></ul><ul><li>Straight Angles have measures equal to 180° </li></ul>
  3. 3. PARALLEL LINES <ul><li>Def: Lines that do not intersect. Parallel lines are always the same distance apart. </li></ul><ul><li>Illustration: </li></ul><ul><li>Notation: l || m AB || CD </li></ul>l m A B C D
  4. 4. PERPENDICULAR LINES <ul><li>Def: Lines that intersect to form a right angle. </li></ul><ul><li>Illustration: </li></ul><ul><li>Notation: m  n </li></ul><ul><li>Key Fact: 4 right angles are formed. </li></ul>m n
  5. 5. <ul><li>Def: A line that intersects two lines at different points. </li></ul><ul><li>Illustration: </li></ul>Transversal t
  6. 6. Vertical Angles <ul><li>Two angles that are opposite angles. </li></ul>1 2 3 4 5 6 7 8 t <ul><li>1   4 </li></ul><ul><li>2   3 </li></ul><ul><li>5   8 </li></ul><ul><li>6   7 </li></ul>
  7. 7. Vertical Angles <ul><li>Find the measures of the missing angles </li></ul>125  ? ? 55  t
  8. 8. Vertical Angles <ul><li>Find the measures of the missing angles </li></ul>125  55  t 55  125 
  9. 9. Angle Relationships <ul><li>Complementary Angles are two angles whose sum is 90°. </li></ul><ul><li>Supplementary Angles are two angles whose sum is 180°. </li></ul><ul><li>Angles do not have </li></ul><ul><li>to be Adjacent to be Complementary or Supplementary. </li></ul><ul><li>Adjacent Angles </li></ul><ul><li>are two angles that share a common side. </li></ul>
  10. 10. Supplementary Angles/ Linear Pair <ul><li>Two angles that form a line (sum=180  ) </li></ul><ul><li>5+  6=180 </li></ul><ul><li>6+  8=180 </li></ul><ul><li>8+  7=180 </li></ul><ul><li>7+  5=180 </li></ul><ul><li>1+  2=180 </li></ul><ul><li>2+  4=180 </li></ul><ul><li>4+  3=180 </li></ul><ul><li>3+  1=180 </li></ul>1 2 3 4 5 6 7 8 t
  11. 11. Supplementary Angles/ Linear Pair <ul><li>Find the measures of the missing angles </li></ul>? 72  ? t 180 - 72
  12. 12. Supplementary Angles/ Linear Pair <ul><li>Find the measures of the missing angles </li></ul>72  t 108  108  180 - 72
  13. 13. Corresponding Angles <ul><li>Two angles that occupy corresponding positions. </li></ul>Top Left t Top Left Top Right Top Right Bottom Right Bottom Right Bottom Left Bottom Left <ul><li>1   5 </li></ul><ul><li>2   6 </li></ul><ul><li>3   7 </li></ul><ul><li>4   8 </li></ul>1 2 3 4 5 6 7 8
  14. 14. Corresponding Angles <ul><li>Find the measures of the missing angles </li></ul>145  ? t 35 
  15. 15. Corresponding Angles <ul><li>Find the measures of the missing angles </li></ul>145  t 35  145 
  16. 16. Alternate Interior Angles <ul><li>Two angles that lie between parallel lines on opposite sides of the transversal </li></ul>t <ul><li>3   6 </li></ul><ul><li>4   5 </li></ul>1 2 3 4 5 6 7 8
  17. 17. Alternate Interior Angles <ul><li>Find the measures of the missing angles </li></ul>82  ? t 98 
  18. 18. Alternate Interior Angles <ul><li>Find the measures of the missing angles </li></ul>82  t 98  82 
  19. 19. Alternate Exterior Angles <ul><li>Two angles that lie outside parallel lines on opposite sides of the transversal </li></ul>t <ul><li>2   7 </li></ul><ul><li>1   8 </li></ul>1 2 3 4 5 6 7 8
  20. 20. Alternate Exterior Angles <ul><li>Find the measures of the missing angles </li></ul>120  ? t 60 
  21. 21. Alternate Exterior Angles <ul><li>Find the measures of the missing angles </li></ul>120  t 60  120 
  22. 22. Consecutive Interior Angles <ul><li>Two angles that lie between parallel lines on the same sides of the transversal </li></ul>t <ul><li>3 +  5 = 180 </li></ul><ul><li>4 +  6 = 180 </li></ul>1 2 3 4 5 6 7 8
  23. 23. Consecutive Interior Angles <ul><li>Find the measures of the missing angles </li></ul>? t 135  180 - 135
  24. 24. Consecutive Interior Angles <ul><li>Find the measures of the missing angles </li></ul>t 135  45  180 - 135
  25. 25. This presentation is a modified version of the Slideshow: “ Lines and Angles 2 ” by Miss Patel. The original Slideshow Presentation can be found at www.worldofteaching.com

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