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Using a Protractor to Measure an Angle

Using a Protractor to Measure an Angle
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2020-04-24 05:57
CircleAngleTrigonometryGeometric Construction
① This example demonstrates how to use a protractor (semicircular tool) to measure an angle, providing an interactive visualization of the angle reading process. ② The core mathematical concept is angle measurement, involving the vertex, sides, and numerical value of the angle, while also implicitly relating angles to arcs and sectors. ③ Construction highlights: Based on the construction summary, GeoGebra commands such as Point, Vector, Sequence, RotateText, Text, Circle, Semicircle, CircleSector, CircleArc, and Angle are used to create the protractor's semicircular scale, angle markers, and dynamic text displays. ④ Suitable for upper elementary or middle school students learning introductory geometry, and also useful for teachers in classroom demonstrations to help students intuitively understand protractor usage and angle concepts.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Vector(A, B) → u
  4. Vector(B, A) → v
  5. Sequence(Segment[((4 * cos(t)), (4 * sin(t))), ((4.3 * cos(t)), (4.3 * sin(t)))], t, 0°, 180°, 1°) → l1
  6. Sequence(Segment[((3.9 * cos(t)), (3.9 * sin(t))), ((4.3 * cos(t)), (4.3 * sin(t)))], t, 0°, 180°, 5°) → l2
  7. RotateText("0", 90°) → text1
  8. RotateText("10", (-(80°))) → text2
  9. RotateText("20", (-(70°))) → text3
  10. RotateText("30", (-(60°))) → text4
  11. RotateText("40", (-(50°))) → text5
  12. RotateText("50", (-(40°))) → text6
  13. RotateText("60", (-(30°))) → text7
  14. RotateText("70", (-(20°))) → text8
  15. RotateText("80", (-(10°))) → text9
  16. Text(90) → text10
  17. Circle((0, 0), 0.1) → c
  18. RotateText("100", 10°) → text11
  19. RotateText("110", 20°) → text12
  20. RotateText("120", 30°) → text13
  21. RotateText("130", 40°) → text14
  22. RotateText("170", 78°) → text20
  23. RotateText("160", 68°) → text17
  24. RotateText("150", 57°) → text16
  25. RotateText("140", 47°) → text15
  26. RotateText("180", 90°) → text18
  27. Circle((0, 0), 3.5) → d
  28. Circle((0, 0), 3.2) → e
  29. RotateText("0", 90°) → text19
  30. RotateText("10", 80°) → text21
  31. RotateText("20", 70°) → text22
  32. RotateText("30", 60°) → text23
  33. RotateText("40", 50°) → text24
  34. RotateText("50", 40°) → text25
  35. RotateText("60", 30°) → text26
  36. RotateText("70", 20°) → text27
  37. RotateText("80", 10°) → text28
  38. RotateText("100", (-(10°))) → text29
  39. RotateText("110", (-(20°))) → text30
  40. RotateText("130", (-(41°))) → text32
  41. RotateText("120", (-(31°))) → text31
  42. RotateText("140", (-(49°))) → text33
  43. RotateText("150", (-(58°))) → text34
  44. RotateText("160", (-(68°))) → text35
  45. RotateText("170", (-(78°))) → text36
  46. RotateText("180", (-(90°))) → text37
  47. Sequence(Segment[((3.75 * cos(t)), (3.75 * sin(t))), ((4.3 * cos(t)), (4.3 * sin(t)))], t, 0°, 180°, 10°) → l3
  48. Semicircle((-5, 0), (5, 0)) → f
  49. Point(f) → F
  50. Vector((0, 0), (0, 4.75)) → w
  51. Point(w) → G
  52. Vector(G, F) → a
  53. Circle(C, 3) → g
  54. Point(a) → I
  55. CircleSector(C, I, H) → h
  56. Point(g) → J
  57. CircleSector(C, J, I) → k
  58. CircleArc(K, M, L) → p
  59. Point(p) → O
  60. Vector(O, P) → b
  61. CircleArc(S, Q, R) → q
  62. Vector(R, T) → j
  63. Vector(C, B) → m
  64. Vector(C, A) → n
  65. Angle(B, C, F) → α