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Section 10-6                       Secants, Tangents, and Angle MeasuresMonday, May 21, 2012
Essential Questions                       How do you find measures of angles                       formed by lines intersec...
Vocabulary & Theorems     1. Secant:     Theorem 10.12 - Two Secants:Monday, May 21, 2012
Vocabulary & Theorems     1. Secant: A line that intersects a circle in exactly        two points     Theorem 10.12 - Two ...
Vocabulary & Theorems     1. Secant: A line that intersects a circle in exactly        two points     Theorem 10.12 - Two ...
Vocabulary & Theorems      Theorem 10.13 - Secant and Tangent:Monday, May 21, 2012
Vocabulary & Theorems      Theorem 10.13 - Secant and Tangent: If a       secant and a tangent intersect at the point of  ...
Vocabulary & Theorems      Theorem 10.14 - Exterior Intersection:Monday, May 21, 2012
Vocabulary & Theorems      Theorem 10.14 - Exterior Intersection: If two       secants, a secant and a tangent, or two    ...
Example 1                         Find x.           a.Monday, May 21, 2012
Example 1                         Find x.           a.                        m∠FDE = 180 − m∠EDHMonday, May 21, 2012
Example 1                           Find x.           a.                          m∠FDE = 180 − m∠EDH                     ...
Example 1                           Find x.           a.                          m∠FDE = 180 − m∠EDH                     ...
Example 1                           Find x.           a.                          m∠FDE = 180 − m∠EDH                     ...
Example 1                           Find x.           a.                          m∠FDE = 180 − m∠EDH                     ...
Example 1                           Find x.           a.                          m∠FDE = 180 − m∠EDH                     ...
Example 1                           Find x.           a.                          m∠FDE = 180 − m∠EDH                     ...
Example 1                         Find x.           b.Monday, May 21, 2012
Example 1                         Find x.           b.                           x = 180 − m∠VZWMonday, May 21, 2012
Example 1                         Find x.           b.                           x = 180 − m∠VZW                          ...
Example 1                         Find x.           b.                           x = 180 − m∠VZW                          ...
Example 1                         Find x.           b.                           x = 180 − m∠VZW                          ...
Example 1                         Find x.           b.                           x = 180 − m∠VZW                          ...
Example 1                         Find x.           b.                           x = 180 − m∠VZW                          ...
Example 1                         Find x.           c.Monday, May 21, 2012
Example 1                         Find x.           c.                                   x + 25                           ...
Example 1                         Find x.           c.                                   x + 25                           ...
Example 1                         Find x.           c.                                   x + 25                           ...
Example 2                       Find each measure.                           = 250°           a. m∠QPS when mPTSMonday, M...
Example 2                       Find each measure.                           = 250°           a. m∠QPS when mPTS         ...
Example 2                       Find each measure.                           = 250°           a. m∠QPS when mPTS         ...
Example 2                       Find each measure.                           = 250°           a. m∠QPS when mPTS         ...
Example 2                       Find each measure.                          b. mBDMonday, May 21, 2012
Example 2                       Find each measure.                          b. mBD                              = 360 − ...
Example 2                       Find each measure.                          b. mBD                              = 360 − ...
Example 2                       Find each measure.                          b. mBD                              = 360 − ...
Example 2                       Find each measure.                          b. mBD                              = 360 − ...
Example 3                       Find each measure.                when m∠AED = 62°           a. mBCMonday, May 21, 2012
Example 3                       Find each measure.                when m∠AED = 62°           a. mBC                      ...
Example 3                       Find each measure.                when m∠AED = 62°           a. mBC                      ...
Example 3                       Find each measure.                when m∠AED = 62°           a. mBC                      ...
Example 3                       Find each measure.                when m∠AED = 62°           a. mBC                      ...
Example 3                       Find each measure.                when m∠AED = 62°           a. mBC                      ...
Example 3                       Find each measure.                when m∠AED = 62°           a. mBC                      ...
Example 3                       Find each measure.                           b. m XYZMonday, May 21, 2012
Example 3                       Find each measure.                           b. m XYZ                                   ...
Example 3                       Find each measure.                           b. m XYZ                                    ...
Example 3                       Find each measure.                           b. m XYZ                                    ...
Example 3                       Find each measure.                           b. m XYZ                                    ...
Check Your Understanding                               p. 731 #1-7Monday, May 21, 2012
Problem SetMonday, May 21, 2012
Problem Set                       p. 732 #9-29 odd, 41, 47             "I hate quotations. Tell me what you know."        ...
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Geometry Section 10-6 1112

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Secants, Tangents, and Angle Measures

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Transcript of "Geometry Section 10-6 1112"

  1. 1. Section 10-6 Secants, Tangents, and Angle MeasuresMonday, May 21, 2012
  2. 2. Essential Questions How do you find measures of angles formed by lines intersecting on or inside a circle? How do you find measure of angles formed by lines intersecting outside the circle?Monday, May 21, 2012
  3. 3. Vocabulary & Theorems 1. Secant: Theorem 10.12 - Two Secants:Monday, May 21, 2012
  4. 4. Vocabulary & Theorems 1. Secant: A line that intersects a circle in exactly two points Theorem 10.12 - Two Secants:Monday, May 21, 2012
  5. 5. Vocabulary & Theorems 1. Secant: A line that intersects a circle in exactly two points Theorem 10.12 - Two Secants: If two secants or chords intersect in the interior of a circle, then the measure of an angle formed is half of the sum of the measure of the arcs intercepted by the angle and its vertical angleMonday, May 21, 2012
  6. 6. Vocabulary & Theorems Theorem 10.13 - Secant and Tangent:Monday, May 21, 2012
  7. 7. Vocabulary & Theorems Theorem 10.13 - Secant and Tangent: If a secant and a tangent intersect at the point of tangency, then the measure of each angle formed is half of the measure of its intercepted arcMonday, May 21, 2012
  8. 8. Vocabulary & Theorems Theorem 10.14 - Exterior Intersection:Monday, May 21, 2012
  9. 9. Vocabulary & Theorems Theorem 10.14 - Exterior Intersection: If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of the intercepted arcsMonday, May 21, 2012
  10. 10. Example 1 Find x. a.Monday, May 21, 2012
  11. 11. Example 1 Find x. a. m∠FDE = 180 − m∠EDHMonday, May 21, 2012
  12. 12. Example 1 Find x. a. m∠FDE = 180 − m∠EDH 76 + 88 m∠EDH = 2Monday, May 21, 2012
  13. 13. Example 1 Find x. a. m∠FDE = 180 − m∠EDH 76 + 88 164 m∠EDH = = 2 2Monday, May 21, 2012
  14. 14. Example 1 Find x. a. m∠FDE = 180 − m∠EDH 76 + 88 164 m∠EDH = = = 82° 2 2Monday, May 21, 2012
  15. 15. Example 1 Find x. a. m∠FDE = 180 − m∠EDH 76 + 88 164 m∠EDH = = = 82° 2 2 m∠FDE = 180 − 82Monday, May 21, 2012
  16. 16. Example 1 Find x. a. m∠FDE = 180 − m∠EDH 76 + 88 164 m∠EDH = = = 82° 2 2 m∠FDE = 180 − 82 = 98°Monday, May 21, 2012
  17. 17. Example 1 Find x. a. m∠FDE = 180 − m∠EDH 76 + 88 164 m∠EDH = = = 82° 2 2 m∠FDE = 180 − 82 = 98° x = 98Monday, May 21, 2012
  18. 18. Example 1 Find x. b.Monday, May 21, 2012
  19. 19. Example 1 Find x. b. x = 180 − m∠VZWMonday, May 21, 2012
  20. 20. Example 1 Find x. b. x = 180 − m∠VZW 96 + 62 m∠VZW = 2Monday, May 21, 2012
  21. 21. Example 1 Find x. b. x = 180 − m∠VZW 96 + 62 m∠VZW = 2 158 = 2Monday, May 21, 2012
  22. 22. Example 1 Find x. b. x = 180 − m∠VZW 96 + 62 m∠VZW = 2 158 = = 79° 2Monday, May 21, 2012
  23. 23. Example 1 Find x. b. x = 180 − m∠VZW 96 + 62 m∠VZW = 2 158 = = 79° 2 x = 180 − 79Monday, May 21, 2012
  24. 24. Example 1 Find x. b. x = 180 − m∠VZW 96 + 62 m∠VZW = 2 158 = = 79° 2 x = 180 − 79 = 101Monday, May 21, 2012
  25. 25. Example 1 Find x. c.Monday, May 21, 2012
  26. 26. Example 1 Find x. c. x + 25 60 = 2Monday, May 21, 2012
  27. 27. Example 1 Find x. c. x + 25 60 = 2 120 = x + 25Monday, May 21, 2012
  28. 28. Example 1 Find x. c. x + 25 60 = 2 120 = x + 25 x = 95Monday, May 21, 2012
  29. 29. Example 2 Find each measure.  = 250° a. m∠QPS when mPTSMonday, May 21, 2012
  30. 30. Example 2 Find each measure.  = 250° a. m∠QPS when mPTS 1  m∠QPS = mPTS 2Monday, May 21, 2012
  31. 31. Example 2 Find each measure.  = 250° a. m∠QPS when mPTS 1  m∠QPS = mPTS 2 1 = (250) 2Monday, May 21, 2012
  32. 32. Example 2 Find each measure.  = 250° a. m∠QPS when mPTS 1  m∠QPS = mPTS 2 1 = (250) = 125° 2Monday, May 21, 2012
  33. 33. Example 2 Find each measure.  b. mBDMonday, May 21, 2012
  34. 34. Example 2 Find each measure.  b. mBD  = 360 − 2m∠ADB mBDMonday, May 21, 2012
  35. 35. Example 2 Find each measure.  b. mBD  = 360 − 2m∠ADB mBD = 360 − 2(108)Monday, May 21, 2012
  36. 36. Example 2 Find each measure.  b. mBD  = 360 − 2m∠ADB mBD = 360 − 2(108) = 360 − 216Monday, May 21, 2012
  37. 37. Example 2 Find each measure.  b. mBD  = 360 − 2m∠ADB mBD = 360 − 2(108) = 360 − 216 = 144°Monday, May 21, 2012
  38. 38. Example 3 Find each measure.  when m∠AED = 62° a. mBCMonday, May 21, 2012
  39. 39. Example 3 Find each measure.  when m∠AED = 62° a. mBC  − mBC mABD  m∠AED = 2Monday, May 21, 2012
  40. 40. Example 3 Find each measure.  when m∠AED = 62° a. mBC  − mBC mABD  m∠AED = 2 141 − x 62 = 2Monday, May 21, 2012
  41. 41. Example 3 Find each measure.  when m∠AED = 62° a. mBC  − mBC mABD  m∠AED = 2 141 − x 62 = 124 = 141 − x 2Monday, May 21, 2012
  42. 42. Example 3 Find each measure.  when m∠AED = 62° a. mBC  − mBC mABD  m∠AED = 2 141 − x 62 = 124 = 141 − x 2 −17 = −xMonday, May 21, 2012
  43. 43. Example 3 Find each measure.  when m∠AED = 62° a. mBC  − mBC mABD  m∠AED = 2 141 − x 62 = 124 = 141 − x 2 −17 = −x x = 17Monday, May 21, 2012
  44. 44. Example 3 Find each measure.  when m∠AED = 62° a. mBC  − mBC mABD  m∠AED = 2 141 − x 62 = 124 = 141 − x 2 −17 = −x  = 17° mBC x = 17Monday, May 21, 2012
  45. 45. Example 3 Find each measure.  b. m XYZMonday, May 21, 2012
  46. 46. Example 3 Find each measure.  b. m XYZ  − m XZ m XYZ  m∠W = 2Monday, May 21, 2012
  47. 47. Example 3 Find each measure.  b. m XYZ  − m XZ m XYZ  m∠W = 2  − 140 m XYZ 40 = 2Monday, May 21, 2012
  48. 48. Example 3 Find each measure.  b. m XYZ  − m XZ m XYZ  m∠W = 2  − 140 m XYZ 40 = 2  − 140 80 = m XYZMonday, May 21, 2012
  49. 49. Example 3 Find each measure.  b. m XYZ  − m XZ m XYZ  m∠W = 2  − 140 m XYZ 40 = 2  − 140 80 = m XYZ  = 220° m XYZMonday, May 21, 2012
  50. 50. Check Your Understanding p. 731 #1-7Monday, May 21, 2012
  51. 51. Problem SetMonday, May 21, 2012
  52. 52. Problem Set p. 732 #9-29 odd, 41, 47 "I hate quotations. Tell me what you know." – Ralph Waldo EmersonMonday, May 21, 2012
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