Angle Measurements

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Angle Measurements

  1. 1. Angles and their Measurements Delaine Sanders www.flicr.com/photos/34669486/N00/40234362
  2. 2. Angle Parts http://www.flickr.com/photos/dcab2/3514913853/
  3. 3. Angle Parts http://www.flickr.com/photos/dcab2/3514913853/ 2 Rays and a Vertex
  4. 4. Angle Parts . B B A B C RAY BC -> RAY BA -> POINT B BC BA
  5. 5. Angle Parts C A B 2
  6. 6. Angle Naming <ul><li> B </li></ul><ul><li> A B C </li></ul><ul><li> C B A </li></ul><ul><li> 2 </li></ul>A B C 2
  7. 7. Angle Naming A B C D 1 2
  8. 8. Angle Naming <ul><li> A D B or  B D A </li></ul><ul><li> B D C or  C D B </li></ul><ul><li> A D C or  C D A </li></ul><ul><li> 1 </li></ul><ul><li> 2 </li></ul>A B C D 1 2
  9. 9. Angle Naming Practice (STOP) A B C D E F G
  10. 10. Measuring Angles <ul><li>Degrees </li></ul>The angle is the amount of rotation from one ray to the other ray.
  11. 11. Measuring Angles
  12. 12. protractor Measuring Angles
  13. 13. protractor Measuring Angles 50 50 – 0 = 50 m  = 50
  14. 14. protractor Measuring Angles 130 130 – 0 = 130 m  = 130
  15. 15. Measuring Angles 50 50 – 0 = 50 180 – 130 = 50
  16. 16. Measuring Angles (STOP) <ul><li>Measuring Angles Practice – image on note sheet </li></ul><ul><li>Note sheet, clear protractors and 6 inch rulers </li></ul><ul><li>Paper Practice </li></ul><ul><li>Measure side angle </li></ul><ul><li>Measure corner angle </li></ul><ul><li>Fold in half, measure corner angle </li></ul>
  17. 17. 0 ° - 90 °                                                                  Acute Angles
  18. 18. Acute Angles http://www.flickr.com/photos/24418961@N05/3524410992/
  19. 19. Acute Angles
  20. 20. 90 ° - 180 °                                                                    Obtuse Angles
  21. 21. Obtuse Angles http://www.flickr.com/photos/enlightenedfellow/1578956556/
  22. 22. Obtuse Angles
  23. 23. = 90 °                                         Right Angles
  24. 24. Right Angle http://www.flickr.com/photos/jefemontana/2317256019/
  25. 25. Right Angle http://www.flickr.com/photos/jefemontana/2317256019/
  26. 26. Straight Angle = 180 ° .
  27. 27. Straight Angle http://www.flickr.com/photos/forevermoosed/469130102/ http://www.flickr.com/photos/bolivar-trindade/3203862834/
  28. 28. Straight Angle
  29. 29. Interior / Exterior Point . A E C D F .
  30. 30. Interior / Exterior Point . A E C D Point A is interior to  D E C Point F is exterior to  D E C Ray EA is interior to  D E C F .
  31. 31. Angle Addition Postulate The sum of the two smaller angles will always equal the measure of the larger angle .
  32. 32. Angle Addition Postulate The sum of the two smaller angles will always equal the measure of the larger angle . m  MRK + m  KRW = m  MRW
  33. 33. Angle Addition Postulate 2 1  1 +  2 =  A B C A B C
  34. 34. Angle Addition Postulate 2 1  1 = 30 – 0 = 30 2 = 70 – 30 = 40 ABC = 30 + 40 = 70   A B C
  35. 35. Angle Addition Postulate http://www.flickr.com/photos/svyates/2415340942/ 1 2 Angle 1 = 2x Angle 2 = x Solve for angle 1
  36. 36. Angle Bisector <ul><li>An angle bisector is a ray that divides an angle into two equal angles. </li></ul>A B C E <ul><li>ABC   CBE </li></ul><ul><li>m  ABC = m  CBE </li></ul>
  37. 37. Bisected Angle http://www.flickr.com/photos/40256716@N00/367560012/
  38. 38. Bisected Angle http://www.flickr.com/photos/40256716@N00/367560012/
  39. 39. Bisected Angle Ray UK bisects angle U. What is the measure of angle U?
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