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Exploring Special Circle Segments: Concepts & Examples

Dive into identifying segments, the radius-diameter relationship, circumferences, real-world applications, and standardized test scenarios in circle geometry. Understand transformations, mathematical practices, and circle vocabulary. Practice solving circle-related problems.

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Exploring Special Circle Segments: Concepts & Examples

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  1. Splash Screen

  2. Five-Minute Check (over Chapter 9) CCSS Then/Now New Vocabulary Key Concept: Special Segments in a Circle Example 1: Identify Segments in a Circle Key Concept: Radius and Diameter Relationships Example 2: Find Radius and Diameter Key Concept: Circle Pairs Example 3: Find Measures in Intersecting Circles Key Concept: Circumference Example 4: Real-World Example: Find Circumference Example 5: Find Diameter and Radius Example 6: Standardized Test Example: Circumference of Circumscribed Polygon Lesson Menu

  3. A. B. C. D. 5-Minute Check 1

  4. A. B. C. D. 5-Minute Check 1

  5. A. B. C. D. 5-Minute Check 2

  6. A. B. C. D. 5-Minute Check 2

  7. A. STW B. VWT C. WVU D. WRS 5-Minute Check 3

  8. A. STW B. VWT C. WVU D. WRS 5-Minute Check 3

  9. ___ Find the length of the image of MN under a dilation with scale factor k = 3 and MN = 9. A. 6 B. 18 C. 24 D. 27 5-Minute Check 4

  10. ___ Find the length of the image of MN under a dilation with scale factor k = 3 and MN = 9. A. 6 B. 18 C. 24 D. 27 5-Minute Check 4

  11. Find the magnitude and direction of for A(4, 2) and B(–2, –1). A. 2.2; 63.4° B. 4.5; 243.4° C. 6.7; 206.6° D. 6.7; 26.6° 5-Minute Check 5

  12. Find the magnitude and direction of for A(4, 2) and B(–2, –1). A. 2.2; 63.4° B. 4.5; 243.4° C. 6.7; 206.6° D. 6.7; 26.6° 5-Minute Check 5

  13. Which of the following transformations does not preserve length? A. dilation B. reflection C. rotation D. translation 5-Minute Check 6

  14. Which of the following transformations does not preserve length? A. dilation B. reflection C. rotation D. translation 5-Minute Check 6

  15. 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

  16. You identified and used parts of parallelograms. • Identify and use parts of a circle. • Solve problems involving the circumference of a circle. Then/Now

  17. circle • concentric circles • circumference • pi () • inscribed • circumscribed • center • radius • chord • diameter Vocabulary

  18. Concept

  19. Identify Segments in a Circle A. Name the circle and identify a radius. Example 1

  20. Identify Segments in a Circle A. Name the circle and identify a radius. Example 1

  21. Identify Segments in a Circle B. Identify a chord and a diameter of the circle. Example 1

  22. Identify Segments in a Circle B. Identify a chord and a diameter of the circle. Example 1

  23. A. B. C. D. A. Name the circle and identify a radius. Example 1

  24. A. B. C. D. A. Name the circle and identify a radius. Example 1

  25. A. B. C. D. B. Which segment is not a chord? Example 1

  26. A. B. C. D. B. Which segment is not a chord? Example 1

  27. Concept

  28. If RT = 21 cm, what is the length of QV? RT is a diameter and QV is a radius. Find Radius and Diameter d = 2r Diameter Formula 21 = 2rd = 21 10.5 = r Simplify. Answer: Example 2

  29. If RT = 21 cm, what is the length of QV? RT is a diameter and QV is a radius. Find Radius and Diameter d = 2r Diameter Formula 21 = 2rd = 21 10.5 = r Simplify. Answer:QV = 10.5 cm Example 2

  30. If QS = 26 cm, what is the length of RV? A. 12 cm B. 13 cm C. 16 cm D. 26 cm Example 2

  31. If QS = 26 cm, what is the length of RV? A. 12 cm B. 13 cm C. 16 cm D. 26 cm Example 2

  32. Concept

  33. Find Measures in Intersecting Circles Example 3

  34. Since the diameter of is 16 units, WY = 8. Similarly, the diameter of is 22 units, so XZ = 11. WZ is part of radius XZ and part of radius WY. Find Measures in Intersecting Circles First, find ZY. WZ + ZY = WY 5 + ZY = 8 ZY = 3 Next, find XY. XZ + ZY = XY 11 + 3 = XY 14 = XY Example 3

  35. Find Measures in Intersecting Circles Answer: Example 3

  36. Find Measures in Intersecting Circles Answer:XY = 14 units Example 3

  37. A. 3 in. B. 5 in. C. 7 in. D. 9 in. Example 3

  38. A. 3 in. B. 5 in. C. 7 in. D. 9 in. Example 3

  39. Concept

  40. Find Circumference CROP CIRCLES A series of crop circles was discovered in Alberta, Canada, on September 4, 1999. The largest of the three circles had a radius of 30 feet. Find its circumference. Since the radius is 30 feet, and d = 2r, the diameter = 2(30) or 60 feet. C = dCircumference formula = (60) Substitution = 60 Simplify. ≈ 188.50 Use a calculator. Answer: Example 4

  41. Find Circumference CROP CIRCLES A series of crop circles was discovered in Alberta, Canada, on September 4, 1999. The largest of the three circles had a radius of 30 feet. Find its circumference. Since the radius is 30 feet, and d = 2r, the diameter = 2(30) or 60 feet. C = dCircumference formula = (60) Substitution = 60 Simplify. ≈ 188.50 Use a calculator. Answer: The circumference of the crop circle is 60 feet or about 188.50 feet. Example 4

  42. The Unisphere is a giant steel globe that sits in Flushing Meadows-Corona Park in Queens, New York. It has a diameter of 120 feet. Find its circumference. A. 377.0 feet B. 392.5 feet C. 408.3 feet D. 422.1 feet Example 4

  43. The Unisphere is a giant steel globe that sits in Flushing Meadows-Corona Park in Queens, New York. It has a diameter of 120 feet. Find its circumference. A. 377.0 feet B. 392.5 feet C. 408.3 feet D. 422.1 feet Example 4

  44. Divide each side by . Find Diameter and Radius Find the diameter and the radius of a circleto the nearest hundredth if the circumference of the circle is 65.4 feet. Circumference Formula Substitution Use a calculator. Example 5

  45. Find Diameter and Radius Radius Formula Use a calculator. Answer: Example 5

  46. Find Diameter and Radius Radius Formula Use a calculator. Answer:d ≈ 20.82 ft; r ≈ 10.41 ft Example 5

  47. Find the radius of a circle to the nearest hundredth if its circumference is 16.8 meters. A. 8.4 m B. 5.35 m C. 2.67 m D. 16.8 m Example 5

  48. Find the radius of a circle to the nearest hundredth if its circumference is 16.8 meters. A. 8.4 m B. 5.35 m C. 2.67 m D. 16.8 m Example 5

  49. Circumference of Circumscribed Polygon Read the Test Item You need to find the diameter of the circle and use it to calculate the circumference. Example 6

  50. Circumference of Circumscribed Polygon Solve the Test Item The radius of the circle is the same length as either leg of the triangle. The legs of the triangle have equal length. Call the length x. Pythagorean Theorem Substitution Simplify. Divide each side by 2. Take the square root of each side. Example 6

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