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Complementary and Supplementary Angles

Complementary and Supplementary Angles
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2022-10-26 17:10
AngleGeometric ConstructionSlider Animation
This example demonstrates how to understand complementary and supplementary angles through geometric construction. The key mathematical concepts include angle definitions, complementary and supplementary angle calculations. Construction involves using GeoGebra commands like Polygon, Angle, Circle, etc. Suitable for students in grades 6-8 for geometry learning or classroom demonstration.

GeoGebra Commands & Parameters

  1. Polygon(I, J, K, L) → q1, i, j, k, l
  2. Vector(C, V) → u
  3. PointIn(q1) → A
  4. Circle(A, 4) → c
  5. Point(c) → B
  6. Segment(A, B) → s11
  7. OrthogonalLine(A, s11) → perpLine
  8. Intersect(c, perpLine, 2) → MCOM
  9. Arc(c, B, MCOM) → complArc
  10. Mirror(B, A) → MSUP
  11. Arc(c, B, MSUP) → supplArc
  12. Point(If[choice ≤ 2, complArc, supplArc]) → B'
  13. Angle(B, A, B') → α
  14. Rotate(D, If[choice ≤ 2, 90° - α, 180° - α], C) → D'
  15. Point(s11) → E
  16. CircleSector(A, E, B') → d
  17. Segment(C, D) → s21
  18. Segment(A, B') → s12
  19. Angle(D, C, D') → β
  20. Segment(C, D') → s22
  21. Point(s21) → F
  22. CircleSector(C, F, D') → e
  23. Vector(A, V) → v
  24. Translate(e, Vector[(u * transSli2)]) → e'
  25. AngularBisector(B, A, B') → labLin1
  26. AngularBisector(D, C, D') → labLin2
  27. Intersect(e, labLin2) → L2,
  28. Translate(C, u) → C'
  29. Translate(C, u) → C'_{1}
  30. Translate(C, Vector[(transSli2 * u)]) → C'_{2}
  31. Translate(D, Vector[(transSli2 * u)]) → D'_{1}
  32. Segment(C'_{2}, D'_{1}) → s21'
  33. Translate(C, Vector[(transSli2 * u)]) → C'_{3}
  34. Translate(D', Vector[(transSli2 * u)]) → D''
  35. Segment(C'_{3}, D'') → s22'
  36. Translate(A, Vector[(transSli1 * v)]) → A'
  37. Translate(B', Vector[(transSli1 * v)]) → B''
  38. Segment(A', B'') → s12'
  39. Translate(A, Vector[(transSli1 * v)]) → A'_{1}
  40. Translate(B, Vector[(transSli1 * v)]) → B'_{1}
  41. Segment(A'_{1}, B'_{1}) → s11'
  42. Translate(d, Vector[(transSli1 * v)]) → d'
  43. Angle(D'', V, B'_{1}) → ang
  44. Rotate(d', (rotAng * rotSli), V) → d''
  45. Rotate(A'_{1}, (rotAng * rotSli), V) → G
  46. Rotate(B'_{1}, (rotAng * rotSli), V) → H
  47. Segment(G, H) → s11''
  48. Rotate(A', (rotAng * rotSli), V) → A''
  49. Rotate(B'', (rotAng * rotSli), V) → B'''
  50. Segment(A'', B''') → s12''
  51. Polygon(A, E, 4) → squa1, f, g, h, m, M, N
  52. Polygon(C, F, 4) → squa2, n, p, q, r, O, P
  53. Translate(squa1, Vector[(transSli1 * v)]) → squa1'
  54. Rotate(squa1', (rotAng * rotSli), V) → squa1''
  55. Translate(squa2, Vector[(transSli2 * u)]) → squa2'
  56. Translate(Polygon[C, F, 4], Vector[(transSli1 * u)]) → squaBlack
  57. Circle(A, 4.3) → cExt
  58. Mirror(B, cExt) → B'_{2}
  59. Segment(B, B'_{2}) → sv11
  60. Mirror(B', cExt) → B''_{1}
  61. Segment(B', B''_{1}) → sv12
  62. Translate(B, Vector[(transSli1 * u)]) → B'_{3}
  63. Translate(B', Vector[(transSli1 * u)]) → B''_{2}
  64. Translate(B', Vector[(transSli1 * v)]) → B''_{3}
  65. Translate(B''_{1}, Vector[(transSli1 * v)]) → Q
  66. Segment(B''_{3}, Q) → sv12'
  67. Translate(B, Vector[(transSli1 * v)]) → B'_{4}
  68. Translate(B'_{2}, Vector[(transSli1 * v)]) → R
  69. Segment(B'_{4}, R) → sv11'
  70. Rotate(B'_{4}, (rotAng * rotSli), V) → S
  71. Rotate(R, (rotAng * rotSli), V) → R'
  72. Segment(S, R') → sv11''
  73. Rotate(B''_{3}, (rotAng * rotSli), V) → T
  74. Rotate(Q, (rotAng * rotSli), V) → Q'
  75. Segment(T, Q') → sv12''
  76. circlePixels(B, 7 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObject1
  77. circlePixels(B', 7 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObject2
  78. Rotate(B, α - 15°, A) → BF

AI Drawing Prompt Reference

Draw a circle with center C and radius 4. Choose a point A on the circle and draw a line segment AC. Construct a perpendicular line to AC, and let it intersect the circle at point MCOM. Draw an arc with center B and radius BMCOM to represent the supplementary angle. Draw two arcs with centers B and A respectively to represent the supplementary and complementary angles. Choose a point B' on the arc corresponding to the selected angle, and draw angle α between A and B'. Rotate point D to form angle β corresponding to angle α. Draw the angle bisectors of angles α and β, and mark their intersection point L2.
The prompt above was compiled from the original drawing commands and is for reference only.