1. Splash Screen

2. Lesson Menu 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

3. Over Lesson 10–1 5-Minute Check 1 Name a radius. A. B. C. D.

4. Over Lesson 10–1 5-Minute Check 2 Name a chord. A.LF B.MF C.OM D.NF ___

5. Over Lesson 10–1 5-Minute Check 3 Name a diameter. A.OM B.OL C.NF D.MF ___ ____ ___

6. Over Lesson 10–1 5-Minute Check 4 A.2 B.3 C.4 D.5 Refer to the figure. Find BC.

7. Over Lesson 10–1 5-Minute Check 5 A.9 B.11 C.13 D.15 Refer to the figure. Find DE.

8. Over Lesson 10–1 5-Minute Check 6 A.6.5 in. B.10.9 in. C.13 in. D.17 in. Find the length of the radius of the circle.

9. CCSS 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.

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

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

12. Concept

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

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

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

16. Concept

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

18. Example 2 Classify Arcs and Find Arc Measures

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

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

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

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

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

24. Concept

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

26. Example 3 Find Arc Measures in Circle Graphs

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

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

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

30. Concept

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

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

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

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

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

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

37. Concept

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

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

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

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

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

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

44. End of the Lesson