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Splash Screen. Five-Minute Check (over Lesson 10–5) CCSS Then/Now New Vocabulary Theorem 10.12 Example 1: Use Intersecting Chords or Secants Theorem 10.13 Example 2: Use Intersecting Secants and Tangents Theorem 10.14 Example 3: Use Tangents and Secants that Intersect Outside a Circle

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 10–5) CCSS Then/Now New Vocabulary Theorem 10.12 Example 1: Use Intersecting Chords or Secants Theorem 10.13 Example 2: Use Intersecting Secants and Tangents Theorem 10.14 Example 3: Use Tangents and Secants that Intersect Outside a Circle Example 4: Real-World Example: Apply Properties of Intersecting Secants Concept Summary: Circle and Angle Relationships Lesson Menu

  3. ___ Determine whether BC is tangent to the given circle. A. yes B. no 5-Minute Check 1

  4. ___ Determine whether BC is tangent to the given circle. A. yes B. no 5-Minute Check 1

  5. ___ Determine whether QR is tangent to the given circle. A. yes B. no 5-Minute Check 2

  6. ___ Determine whether QR is tangent to the given circle. A. yes B. no 5-Minute Check 2

  7. Find x. Assume that segments that appear to be tangent are tangent. A. 10 B. 11 C. 12 D. 13 5-Minute Check 3

  8. Find x. Assume that segments that appear to be tangent are tangent. A. 10 B. 11 C. 12 D. 13 5-Minute Check 3

  9. A. B. C.20 D. Find x. Assume that segments that appear to be tangent are tangent. 5-Minute Check 4

  10. A. B. C.20 D. Find x. Assume that segments that appear to be tangent are tangent. 5-Minute Check 4

  11. ___ ___ SL and SK are tangent to the circle. Find x. A.1 B. C.5 D.44 5 __ 2 5-Minute Check 5

  12. ___ ___ SL and SK are tangent to the circle. Find x. A.1 B. C.5 D.44 5 __ 2 5-Minute Check 5

  13. Content Standards Reinforcement of G.C.4 Construct a tangent line from a point outside a given circle to the circle. Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. 1 Make sense of problems and persevere in solving them. CCSS

  14. You found measures of segments formed by tangents to a circle. • Find measures of angles formed by lines intersecting on or inside a circle. • Find measures of angles formed by lines intersecting outside the circle. Then/Now

  15. secant Vocabulary

  16. Concept

  17. Use Intersecting Chords or Secants A. Find x. Theorem 10.12 Substitution Simplify. Answer: Example 1

  18. Use Intersecting Chords or Secants A. Find x. Theorem 10.12 Substitution Simplify. Answer:x = 82 Example 1

  19. Use Intersecting Chords or Secants B. Find x. Step 1Find mVZW. Theorem 10.12 Substitution Simplify. Example 1

  20. Use Intersecting Chords or Secants Step 2Find mWZX. mWZX = 180 – mVZWDefinition of supplementary angles x = 180 – 79Substitution x = 101 Simplify. Answer: Example 1

  21. Use Intersecting Chords or Secants Step 2Find mWZX. mWZX = 180 – mVZWDefinition of supplementary angles x = 180 – 79Substitution x = 101 Simplify. Answer:x = 101 Example 1

  22. Use Intersecting Chords or Secants C. Find x. Theorem 10.12 Substitution Multiply each side by 2. Subtract 25 from each side. Answer: Example 1

  23. Use Intersecting Chords or Secants C. Find x. Theorem 10.12 Substitution Multiply each side by 2. Subtract 25 from each side. Answer:x = 95 Example 1

  24. A. Find x. A. 92 B. 95 C. 98 D. 104 Example 1

  25. A. Find x. A. 92 B. 95 C. 98 D. 104 Example 1

  26. B. Find x. A. 92 B. 95 C. 97 D. 102 Example 1

  27. B. Find x. A. 92 B. 95 C. 97 D. 102 Example 1

  28. C. Find x. A. 96 B. 99 C. 101 D. 104 Example 1

  29. C. Find x. A. 96 B. 99 C. 101 D. 104 Example 1

  30. Concept

  31. Use Intersecting Secants and Tangents A. Find mQPS. Theorem 10.13 Substitute and simplify. Answer: Example 2

  32. Use Intersecting Secants and Tangents A. Find mQPS. Theorem 10.13 Substitute and simplify. Answer:mQPS= 125 Example 2

  33. B. Use Intersecting Secants and Tangents Theorem 10.13 Substitution Multiply each side by 2. Answer: Example 2

  34. B. Answer: Use Intersecting Secants and Tangents Theorem 10.13 Substitution Multiply each side by 2. Example 2

  35. A. Find mFGI. A. 98 B. 108 C. 112.5 D. 118.5 Example 2

  36. A. Find mFGI. A. 98 B. 108 C. 112.5 D. 118.5 Example 2

  37. B. A. 99 B. 148.5 C. 162 D. 198 Example 2

  38. B. A. 99 B. 148.5 C. 162 D. 198 Example 2

  39. Concept

  40. A. Use Tangents and Secants that Intersect Outside a Circle Theorem 10.14 Substitution Multiply each side by 2. Example 3

  41. Use Tangents and Secants that Intersect Outside a Circle Subtract 141 from each side. Multiply each side by –1. Example 3

  42. Use Tangents and Secants that Intersect Outside a Circle Subtract 141 from each side. Multiply each side by –1. Example 3

  43. B. Use Tangents and Secants that Intersect Outside a Circle Theorem 10.14 Substitution Multiply each side by 2. Example 3

  44. Use Tangents and Secants that Intersect Outside a Circle Add 140 to each side. Example 3

  45. Use Tangents and Secants that Intersect Outside a Circle Add 140 to each side. Example 3

  46. A. A. 23 B. 26 C. 29 D. 32 Example 3

  47. A. A. 23 B. 26 C. 29 D. 32 Example 3

  48. B. A. 194 B. 202 C. 210 D. 230 Example 3

  49. B. A. 194 B. 202 C. 210 D. 230 Example 3

  50. Apply Properties of Intersecting Secants Theorem 10.14 Substitution Example 4

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