1 / 44

Central Angles, Arcs, and Arc Lengths in Circles

Learn how to find measures of central angles, classify arcs, find arc measures, and calculate arc lengths in circles.

hmoreno
Download Presentation

Central Angles, Arcs, and Arc Lengths in Circles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

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

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

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

  8. 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.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

  10. 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

  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. 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. Example 2

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

  23. 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 arcs in a circle is 360. Substitution Simplify. Simplify. Example 3

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

  29. 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 = 58 + 32 Substitution = 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IMJ + mJMK Substitution = 90 + 58 = 148 Example 4

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

  36. 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. 3.56 cm B. 3.77 cm C. 3.98 cm D. 4.21 cm Example 5

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

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

  44. End of the Lesson

More Related