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Secants, Tangents, and Angle Measures

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- 1. Section 10-6 Secants, Tangents, and Angle MeasuresMonday, May 21, 2012
- 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. Vocabulary & Theorems 1. Secant: Theorem 10.12 - Two Secants:Monday, May 21, 2012
- 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. 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. Vocabulary & Theorems Theorem 10.13 - Secant and Tangent:Monday, May 21, 2012
- 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. Vocabulary & Theorems Theorem 10.14 - Exterior Intersection:Monday, May 21, 2012
- 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. Example 1 Find x. a.Monday, May 21, 2012
- 11. Example 1 Find x. a. m∠FDE = 180 − m∠EDHMonday, May 21, 2012
- 12. Example 1 Find x. a. m∠FDE = 180 − m∠EDH 76 + 88 m∠EDH = 2Monday, May 21, 2012
- 13. Example 1 Find x. a. m∠FDE = 180 − m∠EDH 76 + 88 164 m∠EDH = = 2 2Monday, May 21, 2012
- 14. Example 1 Find x. a. m∠FDE = 180 − m∠EDH 76 + 88 164 m∠EDH = = = 82° 2 2Monday, May 21, 2012
- 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. 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. 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. Example 1 Find x. b.Monday, May 21, 2012
- 19. Example 1 Find x. b. x = 180 − m∠VZWMonday, May 21, 2012
- 20. Example 1 Find x. b. x = 180 − m∠VZW 96 + 62 m∠VZW = 2Monday, May 21, 2012
- 21. Example 1 Find x. b. x = 180 − m∠VZW 96 + 62 m∠VZW = 2 158 = 2Monday, May 21, 2012
- 22. Example 1 Find x. b. x = 180 − m∠VZW 96 + 62 m∠VZW = 2 158 = = 79° 2Monday, May 21, 2012
- 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. 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. Example 1 Find x. c.Monday, May 21, 2012
- 26. Example 1 Find x. c. x + 25 60 = 2Monday, May 21, 2012
- 27. Example 1 Find x. c. x + 25 60 = 2 120 = x + 25Monday, May 21, 2012
- 28. Example 1 Find x. c. x + 25 60 = 2 120 = x + 25 x = 95Monday, May 21, 2012
- 29. Example 2 Find each measure. = 250° a. m∠QPS when mPTSMonday, May 21, 2012
- 30. Example 2 Find each measure. = 250° a. m∠QPS when mPTS 1 m∠QPS = mPTS 2Monday, May 21, 2012
- 31. Example 2 Find each measure. = 250° a. m∠QPS when mPTS 1 m∠QPS = mPTS 2 1 = (250) 2Monday, May 21, 2012
- 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. Example 2 Find each measure. b. mBDMonday, May 21, 2012
- 34. Example 2 Find each measure. b. mBD = 360 − 2m∠ADB mBDMonday, May 21, 2012
- 35. Example 2 Find each measure. b. mBD = 360 − 2m∠ADB mBD = 360 − 2(108)Monday, May 21, 2012
- 36. Example 2 Find each measure. b. mBD = 360 − 2m∠ADB mBD = 360 − 2(108) = 360 − 216Monday, May 21, 2012
- 37. Example 2 Find each measure. b. mBD = 360 − 2m∠ADB mBD = 360 − 2(108) = 360 − 216 = 144°Monday, May 21, 2012
- 38. Example 3 Find each measure. when m∠AED = 62° a. mBCMonday, May 21, 2012
- 39. Example 3 Find each measure. when m∠AED = 62° a. mBC − mBC mABD m∠AED = 2Monday, May 21, 2012
- 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. 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. 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. 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. 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. Example 3 Find each measure. b. m XYZMonday, May 21, 2012
- 46. Example 3 Find each measure. b. m XYZ − m XZ m XYZ m∠W = 2Monday, May 21, 2012
- 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. 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. 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. Check Your Understanding p. 731 #1-7Monday, May 21, 2012
- 51. Problem SetMonday, May 21, 2012
- 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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