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解三角形范例

解三角形范例
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2019-04-15 10:07
测试改名0向量三角函数解析几何几何作图
所属专题 MA440
①本范例演示了通过不同已知条件（边边边SSS、边角边SAS、角边角ASA、角角边AAS）解三角形的几何过程；②涉及的核心数学概念包括三角形的构造、角度测量、边长计算、三角函数应用、相似变换与三维向量；③作图要点：使用了Random、If、Point、Segment、Circle、Intersect、Angle、Rotate、Ray等GeoGebra命令与对象，如F7、F6、E2、A11等，实现随机生成三角形并展示不同解法；④适合高中数学教学，用于理解三角形解法的多样性及实际应用。

GeoGebra 命令及参数

  1. Random(1, 10) → E2
  2. Random(1, 10) → E4
  3. Random(1, 7) → randNum
  4. If(randNum ≟ 4, true, false) → SAS
  5. If(randNum ≟ 3, true, false) → AAS
  6. If(randNum ≟ 2, true, false) → ASA
  7. If(randNum ≟ 1, true, false) → SSS
  8. Random(1, 178) → D5
  9. Random(1, 179 - D5) → D6
  10. Random(1, 178) → C5
  11. Random(1, 179 - C5) → C7
  12. Random(1, 10) → B3
  13. Random(1, 10) → B2
  14. Random(B2 + B3 - 1, abs(B2 - B3) + 1) → B4
  15. Random(1, 178) → E6
  16. If(H11 ≟ 180, F12, F11) → E7
  17. Random(10, 110) → F5
  18. Random(1, 10) → D3
  19. Random(1, 10) → C3
  20. Random(3, 10) → F2
  21. Random(5, 10) → F3
  22. If(¬Defined[C17], 0, If[C17 < 0, 0, 1]) → H17
  23. If(H12 ≟ 180, D12, D11) → E5
  24. Point(Circle[A, B2]) → B
  25. Segment(A, B) → f
  26. Circle(A, B3) → c
  27. Circle(B, B4) → d
  28. Intersect(c, d, 1) → C
  29. Segment(A, C) → g
  30. Segment(B, C) → h
  31. Angle(B, A, C) → α
  32. Angle(C, B, A) → β
  33. Angle(A, C, B) → γ
  34. Point(Circle[D, C3]) → E
  35. Segment(D, E) → i
  36. Rotate(D, (-(C5°)), E) → D'
  37. Angle(D', E, D) → δ
  38. Rotate(E, C7°, D) → E'
  39. Angle(E, D, E') → ε
  40. Ray(D, E') → j
  41. Ray(E, D') → k
  42. Intersect(j, k) → F
  43. Segment(D, F) → l
  44. Segment(F, E) → m
  45. Angle(D, F, E) → ζ
  46. Point(Circle[G, D3]) → H
  47. Segment(G, H) → n
  48. Rotate(H, D5°, G) → H'
  49. Angle(H, G, H') → η
  50. Ray(G, H') → p
  51. Point(p) → I
  52. Rotate(G, D6°, I) → G'
  53. Angle(G, I, G') → θ
  54. Ray(I, G') → q
  55. Circle(G, D4) → e
  56. Intersect(e, p, 1) → J
  57. Segment(G, J) → r
  58. Segment(H, J) → s
  59. Angle(J, H, G) → ι
  60. Angle(G, J, H) → κ
  61. Point(Circle[K, E2]) → L
  62. Segment(K, L) → t
  63. Rotate(L, E6°, K) → L'
  64. Angle(L, K, L') → λ
  65. Ray(K, L') → a
  66. Circle(K, E4) → c_1
  67. Intersect(c_1, a, 1) → M
  68. Segment(K, M) → b
  69. Segment(M, L) → f_1
  70. Angle(K, M, L) → μ
  71. Angle(M, L, K) → ν
  72. If(randNum > 4, true, false) → SSA
  73. Point(Circle[N, F2]) → O
  74. Segment(N, O) → g_1
  75. Point(Circle[N, F3]) → P
  76. Segment(N, P) → h_1
  77. Rotate(N, (-(F5°)), P) → N'
  78. Angle(N', P, N) → ξ
  79. If(C18 < 0, 0, If[A18 ≟ B18, 0, If[Defined[C18], 1, 0]]) → H18
  80. Ray(P, N') → i_1
  81. If(SSAnumTri ≟ 0, true, false) → SSAnoTri
  82. If(SSA ≟ true, If[H17 ≟ 1, true, false], false) → SSA1
  83. If(SSA ≟ true, If[H18 ≟ 1, true, false], false) → SSA2
  84. Circle(P, G4) → d_1
  85. Intersect(d_1, i_1, 1) → Q
  86. Segment(P, Q) → j_1
  87. Segment(N, Q) → k_1
  88. Angle(N, Q, P) → ο
  89. Angle(P, N, Q) → ρ
  90. Circle(P, H4) → e_1
  91. Intersect(e_1, j_1, 1) → R
  92. Segment(N, R) → l_1
  93. Segment(R, P) → m_1
  94. Segment(N, P) → n_1
  95. Angle(P, N, R) → σ
  96. Angle(N, R, P) → τ
  97. If(SSS ≟ true, B2, If[ASA ≟ true, If[showSolution ≟ true, C2, NaN], If[AAS ≟ true, If[showSolution ≟ true, D2, NaN], If[SAS ≟ true, E2, F2]]]) → smallA
  98. If(SSS ≟ true, B4, If[ASA ≟ true, If[showSolution ≟ true, C4, NaN], If[AAS ≟ true, If[showSolution ≟ true, D4, NaN], If[SAS ≟ true, E4, If[showSolution ≟ true, G4, NaN]]]]) → smallC
  99. If(SSS ≟ true, B3, If[ASA ≟ true, C3, If[AAS ≟ true, D3, If[SAS ≟ true, If[showSolution ≟ true, E3, NaN], G3]]]) → smallB
  100. If(SSS ≟ true, If[showSolution ≟ true, B6, NaN], If[ASA ≟ true, If[showSolution ≟ true, C6, NaN], If[AAS ≟ true, D6, If[SAS ≟ true, E6, If[showSolution ≟ true, G6, NaN]]]]) → bigB
  101. If(SSS ≟ true, If[showSolution ≟ true, B7, NaN], If[ASA ≟ true, C7, If[AAS ≟ true, If[showSolution ≟ true, D7, NaN], If[SAS ≟ true, If[showSolution ≟ true, E2, NaN], If[showSolution ≟ true, G7, NaN]]]]) → bigC
  102. If(SSS ≟ true, If[showSolution ≟ true, B5, NaN], If[ASA ≟ true, C5, If[AAS ≟ true, D5, If[SAS ≟ true, If[showSolution ≟ true, E5, NaN], F5]]]) → bigA
  103. If(showSolution ≟ true, ((smallA * smallB) * sin((bigC * π / 180)) / 2), NaN) → area