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5-Minute Check 4

A B C D. Refer to the figure. Find BC. 3. 5-Minute Check 4. A B C D. Refer to the figure. Find DE. 13. 5-Minute Check 5. A B C D. Find the length of the radius of the circle. 6.5 in. 5-Minute Check 6.

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5-Minute Check 4

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

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

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

  4. Identify central angles, major arcs, minor arcs, and semicircles, and find their measures. • Find arc lengths. Then/Now

  5. central angle—an angle with a vertex in the center of the cricle • arc—a portion of a circle defined by two endpoints on the circle. An arc has the same measure of the central angle formed by its endpoints. Vocabulary

  6. Concept

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

  8. 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

  9. A B C D Find the value of x. 9 Example 1

  10. Concept

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

  12. Classify Arcs and Find Arc Measures Example 2

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

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

  15. A B C D Example 2

  16. A B C D Example 2

  17. A B C D Example 2

  18. congruent arcs—arcs in the same or congruent circles that have the same measure.

  19. Concept

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

  21. Find Arc Measures in Circle Graphs Example 3

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

  23. A B C D 140.4 Example 3

  24. A B C D 273.6 Example 3

  25. adjacent arcs—arcs in a circle that have exactly one endpoint in common.

  26. Concept

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

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

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

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

  31. A B C D 52 Example 4

  32. A B C D 142 Example 4

  33. arc length—the distance between the endpoints along an arc measured in linear units. Since an arc is a portion of a circle, its length is a fraction of the circumference.

  34. Concept

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

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

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

  38. A B C D 3.77 cm Example 5

  39. A B C D 38.61 cm Example 5

  40. A B C D 32.99 cm Example 5

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