Geometry Section 1-4 1112

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Geometry Section 1-4 1112

  1. 1. Section 1-4 Angle Measure Monday, September 15, 14
  2. 2. Essential Questions ✤ How do you measure and classify angles? ✤ How do you identify and use congruent angles and the bisector of an angle? Monday, September 15, 14
  3. 3. Vocabulary 1. Ray: 2. Opposite Rays: 3. Angle: 4. Side: 5. Vertex: 6. Interior: Monday, September 15, 14
  4. 4. Vocabulary 1. R a y : Part of a line; has an endpoint and goes on forever in one direction; ray AB: AB 2. Opposite Rays: 3. Angle: 4. Side: 5. Vertex: 6. Interior: Monday, September 15, 14
  5. 5. Vocabulary 1. R a y : Part of a line; has an endpoint and goes on forever in one direction; ray AB: AB 2. Opposite Rays: Rays that share an endpoint and are collinear 3. Angle: 4. Side: 5. Vertex: 6. Interior: Monday, September 15, 14
  6. 6. Vocabulary 1. R a y : Part of a line; has an endpoint and goes on forever in one direction; ray AB: AB 2. Opposite Rays: Rays that share an endpoint and are collinear 3. An g l e : Two noncollinear rays that share an endpoint; uses three points or a listed number to name ∠ABC or ∠5 4. Side: 5. Vertex: 6. Interior: Monday, September 15, 14
  7. 7. Vocabulary 1. R a y : Part of a line; has an endpoint and goes on forever in one direction; ray AB: AB 2. Opposite Rays: Rays that share an endpoint and are collinear 3. An g l e : Two noncollinear rays that share an endpoint; uses three points or a listed number to name ∠ABC or ∠5 4. Side: One of the rays that makes up an angle 5. Vertex: 6. Interior: Monday, September 15, 14
  8. 8. Vocabulary 1. R a y : Part of a line; has an endpoint and goes on forever in one direction; ray AB: AB 2. Opposite Rays: Rays that share an endpoint and are collinear 3. An g l e : Two noncollinear rays that share an endpoint; uses three points or a listed number to name ∠ABC or ∠5 4. Side: One of the rays that makes up an angle 5. Vertex: The shared endpoint of the two rays that make up an angle 6. Interior: Monday, September 15, 14
  9. 9. Vocabulary 1. R a y : Part of a line; has an endpoint and goes on forever in one direction; ray AB: AB 2. Opposite Rays: Rays that share an endpoint and are collinear 3. An g l e : Two noncollinear rays that share an endpoint; uses three points or a listed number to name ∠ABC or ∠5 4. Side: One of the rays that makes up an angle 5. Vertex: The shared endpoint of the two rays that make up an angle 6. I n t e r i o r : The part of an angle that is inside the two rays of the angle (the part that is less than 180° in measure) Monday, September 15, 14
  10. 10. Vocabulary 7. Exterior: 8. Degree: 9. Right Angle: 10. Acute Angle: 11. Obtuse Angle: 12. Angle Bisector: Monday, September 15, 14
  11. 11. Vocabulary 7. E x t e r i o r : The part of an angle that is outside the two rays of the angle (the part that is greater than 180° in measure) 8. Degree: 9. Right Angle: 10. Acute Angle: 11. Obtuse Angle: 12. Angle Bisector: Monday, September 15, 14
  12. 12. Vocabulary 7. E x t e r i o r : The part of an angle that is outside the two rays of the angle (the part that is greater than 180° in measure) 8. Degree: The unit of measurement of an angle 9. Right Angle: 10. Acute Angle: 11. Obtuse Angle: 12. Angle Bisector: Monday, September 15, 14
  13. 13. Vocabulary 7. E x t e r i o r : The part of an angle that is outside the two rays of the angle (the part that is greater than 180° in measure) 8. Degree: The unit of measurement of an angle 9. Right Angle: An angle that is 90° in measure 10. Acute Angle: 11. Obtuse Angle: 12. Angle Bisector: Monday, September 15, 14
  14. 14. Vocabulary 7. E x t e r i o r : The part of an angle that is outside the two rays of the angle (the part that is greater than 180° in measure) 8. Degree: The unit of measurement of an angle 9. Right Angle: An angle that is 90° in measure 10. Acute Angle: An angle that is less than 90° in measure 11. Obtuse Angle: 12. Angle Bisector: Monday, September 15, 14
  15. 15. Vocabulary 7. E x t e r i o r : The part of an angle that is outside the two rays of the angle (the part that is greater than 180° in measure) 8. Degree: The unit of measurement of an angle 9. Right Angle: An angle that is 90° in measure 10. Acute Angle: An angle that is less than 90° in measure 11. Obtuse Angle: An angle that is more than 90° in measure 12. Angle Bisector: Monday, September 15, 14
  16. 16. Vocabulary 7. E x t e r i o r : The part of an angle that is outside the two rays of the angle (the part that is greater than 180° in measure) 8. Degree: The unit of measurement of an angle 9. Right Angle: An angle that is 90° in measure 10. Acute Angle: An angle that is less than 90° in measure 11. Obtuse Angle: An angle that is more than 90° in measure 1 2 . A n g l e B i s e c t o r : A ray and splits an angle into two parts with equal measure Monday, September 15, 14
  17. 17. Example 1 Use the figure. a. Name all angles that have C as a vertex. b. Name the sides of ∠7. c. Write another name for ∠4. Monday, September 15, 14
  18. 18. Example 1 Use the figure. a. Name all angles that have C as a vertex. ∠ACB,∠BCD,∠DCG,∠GCA b. Name the sides of ∠7. c. Write another name for ∠4. Monday, September 15, 14
  19. 19. Example 1 Use the figure. a. Name all angles that have C as a vertex. ∠ACB,∠BCD,∠DCG,∠GCA b. Name the sides of ∠7. DE, DF c. Write another name for ∠4. Monday, September 15, 14
  20. 20. Example 1 Use the figure. a. Name all angles that have C as a vertex. ∠ACB,∠BCD,∠DCG,∠GCA b. Name the sides of ∠7. DE, DF c. Write another name for ∠4. ∠IGD Monday, September 15, 14
  21. 21. Example 2 Use the figure. Measure the angles listed and classify as either acute, right, or obtuse. a. m∠AFC b. m∠EFB c. m∠EFD Monday, September 15, 14
  22. 22. Example 2 Use the figure. Measure the angles listed and classify as either acute, right, or obtuse. a. m∠AFC b. m∠EFB c. m∠EFD http://www.chutedesign.co.uk/design/protractor/protractor.gif Monday, September 15, 14
  23. 23. Example 2 Use the figure. Measure the angles listed and classify as either acute, right, or obtuse. a. m∠AFC b. m∠EFB c. m∠EFD http://www.chutedesign.co.uk/design/protractor/protractor.gif Monday, September 15, 14
  24. 24. Example 2 Use the figure. Measure the angles listed and classify as either acute, right, or obtuse. a. m∠AFC b. m∠EFB c. m∠EFD http://www.chutedesign.co.uk/design/protractor/protractor.gif 90°, Right Monday, September 15, 14
  25. 25. Example 2 Use the figure. Measure the angles listed and classify as either acute, right, or obtuse. a. m∠AFC b. m∠EFB c. m∠EFD http://www.chutedesign.co.uk/design/protractor/protractor.gif 90°, Right Monday, September 15, 14
  26. 26. Example 2 Use the figure. Measure the angles listed and classify as either acute, right, or obtuse. a. m∠AFC b. m∠EFB c. m∠EFD http://www.chutedesign.co.uk/design/protractor/protractor.gif 90°, Right Monday, September 15, 14
  27. 27. Example 2 Use the figure. Measure the angles listed and classify as either acute, right, or obtuse. a. m∠AFC b. m∠EFB c. m∠EFD http://www.chutedesign.co.uk/design/protractor/protractor.gif 90°, Right 165°, Obtuse Monday, September 15, 14
  28. 28. Example 2 Use the figure. Measure the angles listed and classify as either acute, right, or obtuse. a. m∠AFC b. m∠EFB c. m∠EFD http://www.chutedesign.co.uk/design/protractor/protractor.gif 90°, Right 165°, Obtuse 51°, Acute Monday, September 15, 14
  29. 29. Example 3 GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR. Monday, September 15, 14
  30. 30. Example 3 GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR. H G J Monday, September 15, 14
  31. 31. B Example 3 GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR. H G J Monday, September 15, 14
  32. 32. R B Example 3 GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR. H G J Monday, September 15, 14
  33. 33. R B Example 3 GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR. H G J Monday, September 15, 14
  34. 34. R B Example 3 GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR. H G J Monday, September 15, 14
  35. 35. R B Example 3 GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR. 9x − 7 H G J Monday, September 15, 14
  36. 36. R B Example 3 GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR. 9x − 7 7x + 13 H G J Monday, September 15, 14
  37. 37. R B Example 3 GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR. 9x − 7 7x + 13 H G J 9x − 7 = 7x + 13 Monday, September 15, 14
  38. 38. R B Example 3 GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR. 9x − 7 7x + 13 H G J 9x − 7 = 7x + 13 − 7x − 7x Monday, September 15, 14
  39. 39. R B Example 3 GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR. 9x − 7 7x + 13 H G J 9x − 7 = 7x + 13 − 7x + 7 − 7x + 7 Monday, September 15, 14
  40. 40. R B Example 3 GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR. 9x − 7 7x + 13 H G J 9x − 7 = 7x + 13 − 7x + 7 − 7x + 7 Monday, September 15, 14
  41. 41. R B Example 3 GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR. 9x − 7 7x + 13 H G J 9x − 7 = 7x + 13 − 7x + 7 − 7x + 7 2x = 20 Monday, September 15, 14
  42. 42. R B Example 3 GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR. 9x − 7 7x + 13 H G J 9x − 7 = 7x + 13 − 7x + 7 − 7x + 7 2x = 20 2 2 Monday, September 15, 14
  43. 43. R B Example 3 GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR. 9x − 7 7x + 13 H G J 9x − 7 = 7x + 13 − 7x + 7 − 7x + 7 2x = 20 2 2 x = 10 Monday, September 15, 14
  44. 44. R B Example 3 GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR. 9x − 7 7x + 13 H G J 9x − 7 = 7x + 13 − 7x + 7 − 7x + 7 2x = 20 2 2 x = 10 m∠HGR = 9(10) − 7 Monday, September 15, 14
  45. 45. R B Example 3 GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR. 9x − 7 7x + 13 H G J 9x − 7 = 7x + 13 − 7x + 7 − 7x + 7 2x = 20 2 2 x = 10 m∠HGR = 9(10) − 7 = 90 − 7 Monday, September 15, 14
  46. 46. R B Example 3 GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR. 9x − 7 7x + 13 H G J 9x − 7 = 7x + 13 − 7x + 7 − 7x + 7 2x = 20 2 2 x = 10 m∠HGR = 9(10) − 7 = 90 − 7 = 83° Monday, September 15, 14
  47. 47. Problem Set Monday, September 15, 14
  48. 48. Problem Set p. 41 #1-41 odd, 51 “If we all did the things we are capable of doing, we would literally astound ourselves.” - Thomas A. Edison Monday, September 15, 14

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