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Splash Screen. Five-Minute Check (over Lesson 10–1) CCSS Then/Now New Vocabulary Key Concept: Sum of Central Angles Example 1: Find Measures of Central Angles Key Concept: Arcs and Arc Measure Example 2: Classify Arcs and Find Arc Measures Theorem 10.1

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 10–1) CCSS Then/Now New Vocabulary Key Concept: Sum of Central Angles Example 1: Find Measures of Central Angles Key Concept: Arcs and Arc Measure Example 2: Classify Arcs and Find Arc Measures Theorem 10.1 Example 3: Real-World Example: Find Arc Measures in Circle Graphs Postulate 10.1: Arc Addition Postulate Example 4: Use Arc Addition to Find Measures of Arcs Key Concept: Arc Length Example 5: Find Arc Length Lesson Menu

  3. Name a radius. A. B. C. D. 5-Minute Check 1

  4. Name a radius. A. B. C. D. 5-Minute Check 1

  5. Name a chord. ___ A.LF B.MF C.OM D.NF ___ ___ ___ 5-Minute Check 2

  6. Name a chord. ___ A.LF B.MF C.OM D.NF ___ ___ ___ 5-Minute Check 2

  7. Name a diameter. ____ A.OM B.OL C.NF D.MF ___ ___ ____ 5-Minute Check 3

  8. Name a diameter. ____ A.OM B.OL C.NF D.MF ___ ___ ____ 5-Minute Check 3

  9. Refer to the figure. Find BC. A. 2 B. 3 C. 4 D. 5 5-Minute Check 4

  10. Refer to the figure. Find BC. A. 2 B. 3 C. 4 D. 5 5-Minute Check 4

  11. Refer to the figure. Find DE. A. 9 B. 11 C. 13 D. 15 5-Minute Check 5

  12. Refer to the figure. Find DE. A. 9 B. 11 C. 13 D. 15 5-Minute Check 5

  13. Find the length of the radius of the circle. A. 6.5 in. B. 10.9 in. C. 13 in. D. 17 in. 5-Minute Check 6

  14. Find the length of the radius of the circle. A. 6.5 in. B. 10.9 in. C. 13 in. D. 17 in. 5-Minute Check 6

  15. Content Standards G.C.2 Identify and describe relationships among inscribed angles, radii, and chords. G.C.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Mathematical Practices 6 Attend to precision. 4 Model with mathematics. CCSS

  16. You measured angles and identified congruent angles. • Identify central angles, major arcs, minor arcs, and semicircles, and find their measures. • Find arc lengths. Then/Now

  17. central angle • arc length • arc • minor arc • major arc • semicircle • congruent arcs • adjacent arcs Vocabulary

  18. Concept

  19. Find Measures of Central Angles Find the value of x. Example 1

  20. The sum of the measures of Find Measures of Central Angles Substitution Simplify. Add 2 to each side. Divide each side by 26. Answer: Example 1

  21. The sum of the measures of Find Measures of Central Angles Substitution Simplify. Add 2 to each side. Divide each side by 26. Answer:x = 7 Example 1

  22. Find the value of x. A. 9 B. 10 C. 11 D. 65 Example 1

  23. Find the value of x. A. 9 B. 10 C. 11 D. 65 Example 1

  24. Concept

  25. Classify Arcs and Find Arc Measures Answer: Example 2

  26. Answer: Classify Arcs and Find Arc Measures Example 2

  27. Classify Arcs and Find Arc Measures Example 2

  28. Classify Arcs and Find Arc Measures Answer: Example 2

  29. Answer: Classify Arcs and Find Arc Measures Example 2

  30. Classify Arcs and Find Arc Measures Answer: Example 2

  31. Answer: Classify Arcs and Find Arc Measures Example 2

  32. A. B. C. D. Example 2

  33. A. B. C. D. Example 2

  34. A. B. C. D. Example 2

  35. A. B. C. D. Example 2

  36. A. B. C. D. Example 2

  37. A. B. C. D. Example 2

  38. Concept

  39. Find Arc Measures in Circle Graphs mLPK = 0.21(360) Find 21% of 360. = 75.6 Simplify. Answer: Example 3

  40. Answer: Find Arc Measures in Circle Graphs mLPK = 0.21(360) Find 21% of 360. = 75.6 Simplify. Example 3

  41. Find Arc Measures in Circle Graphs Example 3

  42. Find Arc Measures in Circle Graphs Sum of arcs in a circle is 360. Substitution Simplify. Simplify. Answer: Example 3

  43. Answer: Find Arc Measures in Circle Graphs Sum of arcs in a circle is 360. Substitution Simplify. Simplify. Example 3

  44. A. 124.3 B. 140.4 C. 155.6 D. 165.9 Example 3

  45. A. 124.3 B. 140.4 C. 155.6 D. 165.9 Example 3

  46. A. 273.6 B. 240.5 C. 215.7 D. 201.4 Example 3

  47. A. 273.6 B. 240.5 C. 215.7 D. 201.4 Example 3

  48. Concept

  49. . Use Arc Addition to Find Measures of Arcs Example 4

  50. Use Arc Addition to Find Measures of Arcs Arc Addition Postulate = 58 + 32 Substitution = 90 Answer: Example 4

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