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 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 in.
C. 13 in.
D. 17 in.
5-Minute Check 6

15. Mathematical Practices 6 Attend to precision.
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
The sum of the measures of
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
The sum of the measures of
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. Classify Arcs and Find Arc Measures
Answer:
Example 2

27. Classify Arcs and Find Arc Measures
Example 2

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

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

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

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

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

41. Find Arc Measures in Circle Graphs
Example 3

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

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

44. A B C D
Example 3

45. A B C D
Example 3

46. A B C D
Example 3

47. A B C D
Example 3

48. Concept

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

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

51. Arc Addition Postulate
Use Arc Addition to Find Measures of Arcs
Arc Addition Postulate =
Substitution
= 90
Answer:
Example 4

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

53. Arc Addition Postulate
Use Arc Addition to Find Measures of Arcs
Arc Addition Postulate
= mIMJ + mJMK =
Substitution
= 148
Answer:
Example 4

54. Arc Addition Postulate
Use Arc Addition to Find Measures of Arcs
Arc Addition Postulate
= mIMJ + mJMK =
Substitution
= 148
Answer:
Example 4

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

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

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

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

59. Concept

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

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

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

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

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

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

66. A cm
B cm
C cm
D cm
Example 5

67. A cm
B cm
C cm
D cm
Example 5

68. A cm
B cm
C cm
D cm
Example 5

69. A cm
B cm
C cm
D cm
Example 5

70. A cm
B cm
C cm
D cm
Example 5

71. A cm
B cm
C cm
D cm
Example 5

72. End of the Lesson