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Splash Screen. Five-Minute Check (over Lesson 10–1) 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) 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. A B C D Name a radius. A. B. C. D. 5-Minute Check 1

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

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

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

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

  8. A B C D 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

  9. Content Standards G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G.C.1 Prove that all circles are similar. Mathematical Practices 4 Model with mathematics. 1 Make sense of problems and persevere in solving them. CCSS

  10. You measured angles and identified congruent angles. (Lesson 1–4) • Identify central angles, major arcs, minor arcs, and semicircles, and find their measures. • Find arc lengths. Then/Now

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

  12. Concept

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

  14. 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

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

  16. Concept

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

  18. Classify Arcs and Find Arc Measures Example 2

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

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

  21. A B C D A. B. C. D. Example 2

  22. A B C D A. B. C. D. Example 2

  23. A B C D A. B. C. D. Example 2

  24. Concept

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

  26. Find Arc Measures in Circle Graphs Example 3

  27. Answer: Find Arc Measures in Circle Graphs Sum of arc in circle is 360. Substitution Simplify. Simplify. Example 3

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

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

  30. Concept

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

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

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

  34. Answer: Use Arc Addition to Find Measures of Arcs Arc Addition Postulate = mIJ + mJK Substitution = 90 + 58 = 148 Example 4

  35. A B C D A. 38 B. 52 C. 90 D. 180 Example 4

  36. A B C D A. 52 B. 90 C. 142 D. 180 Example 4

  37. Concept

  38. cm Use a calculator. Answer: Find Arc Length Arc Length Equation Substitution Example 5

  39. Answer: Find Arc Length Arc Length Equation Substitution Use a calculator. Example 5

  40. Answer: Find Arc Length Arc Length Equation Substitution Use a calculator. Example 5

  41. A B C D A. 3.56 cm B. 3.77 cm C. 3.98 cm D. 4.21 cm Example 5

  42. A B C D A. 36.56 cm B. 37.79 cm C. 38.61 cm D. 40.21 cm Example 5

  43. A B C D A. 32.99 cm B. 33.59 cm C. 33.89 cm D. 34.61 cm Example 5

  44. End of the Lesson

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