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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