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平行四边形几何任务：内切圆与三角函数综合探究

平行四边形几何任务：内切圆与三角函数综合探究
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2016-10-12 03:40
圆多边形角三角函数几何作图
该范例演示了一个包含平行四边形、内切圆、三角函数及线性方程的综合几何构造。核心数学概念包括平行四边形的性质、内切圆与切线、角度测量、距离计算以及三角函数关系。作图要点：使用GeoGebra的Segment、Line、Intersect、OrthogonalLine、Point、Circle、Angle、Distance等命令，构建了多个点（A, D, B, C, E, F, G, H, I, J, K等）、线段、直线、垂线、圆以及角度对象（α, β, γ, δ, ε），并利用文本对象（text1, text2, text3）标注信息。该任务适合高中或大学低年级学生，用于深入理解几何图形与三角函数的联系，以及动态几何软件中的构造与测量技巧。

GeoGebra 命令及参数

  1. Segment(A, D) → f
  2. Segment(A, B) → g
  3. Line(B, f) → h
  4. Line(D, g) → i
  5. Intersect(h, i) → C
  6. Segment(B, C) → j
  7. Segment(D, C) → k
  8. Segment(E, H_1) → l
  9. OrthogonalLine(E, l) → m
  10. Point(m) → F
  11. Segment(F, E) → n
  12. Line(F, l) → p
  13. Line(H_1, n) → q
  14. Intersect(p, q) → G
  15. Segment(F, G) → r
  16. Segment(H_1, G) → s
  17. Segment(H, K) → t
  18. Circle(H, t) → c
  19. Point(c) → I
  20. Segment(H, I) → a
  21. Line(I, t) → b
  22. Line(K, a) → d
  23. Intersect(b, d) → J
  24. Segment(J, I) → e
  25. Segment(J, K) → f_1
  26. Angle(D, A, B) → α
  27. Angle(A, B, C) → β
  28. Angle(B, C, D) → γ
  29. Angle(C, D, A) → δ
  30. Angle(E, F, G) → ε
  31. Angle(G, H_1, E) → ζ
  32. Angle(H_1, E, F) → η
  33. Angle(F, G, H_1) → θ
  34. Angle(H, I, J) → ι
  35. Angle(I, J, K) → κ
  36. Angle(J, K, H) → λ
  37. Angle(K, H, I) → μ
  38. Distance(A, B) → distanceAB
  39. Distance(B, C) → distanceBC
  40. Distance(C, D) → distanceCD
  41. Distance(D, A) → distanceDA
  42. Distance(F, G) → distanceFG
  43. Distance(G, H_1) → distanceGH1
  44. Distance(H_1, E) → distanceH1E
  45. Distance(E, F) → distanceEF
  46. Distance(I, J) → distanceIJ
  47. Distance(J, K) → distanceJK
  48. Distance(K, H) → distanceKH
  49. Distance(H, I) → distanceHI
  50. Segment(A, C) → g_1
  51. Segment(B, D) → h_1
  52. Segment(F, H_1) → i_1
  53. Segment(G, E) → j_1
  54. Segment(H, J) → k_1
  55. Segment(K, I) → l_1
  56. Intersect(g_1, h_1) → L
  57. Intersect(j_1, i_1) → M
  58. Intersect(l_1, k_1) → Q
  59. Distance(A, L) → distanceAL
  60. Distance(B, L) → distanceBL
  61. Distance(L, D) → distanceLD
  62. Distance(C, L) → distanceCL
  63. Distance(F, M) → distanceFM
  64. Distance(M, G) → distanceMG
  65. Distance(H_1, M) → distanceH1M
  66. Distance(M, E) → distanceME
  67. Distance(H, Q) → distanceHN
  68. Distance(I, Q) → distanceIN
  69. Distance(J, Q) → distanceJN
  70. Distance(K, Q) → distanceKN
  71. Distance(E, G) → distanceEG
  72. Distance(F, H_1) → distanceFH1
  73. Angle(J, Q, I) → AngleJQI
  74. Angle(I, K, H) → ν
  75. Angle(J, K, I) → ξ
  76. Angle(H, I, Q) → ο
  77. Angle(K, I, J) → ρ
  78. Angle(I, J, H) → σ
  79. Angle(H, J, K) → τ
  80. Angle(J, H, I) → υ
  81. Angle(K, H, J) → ϕ