特殊直角三角形游戏

特殊直角三角形游戏
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2016-05-23 09:28
①本范例演示特殊直角三角形(30°-60°-90°和45°-45°-90°)的构造与性质;②涉及核心数学概念包括直角三角形、三角函数、比例关系、分数、几何变换等;③构造过程中运用了Segment、Point、Midpoint、Rotate、Line、Intersect、Mirror、Polygon、Angle、Textfield、OrthogonalLine、Element、LaTeX等GeoGebra命令与对象;④适合初中及以上数学学习者,用于理解和应用特殊直角三角形的几何与三角知识。

GeoGebra 命令及参数

  1. Segment(B, A) → d
  2. Segment(C, B) → p
  3. Segment(D, A) → k
  4. Point(k) → F
  5. Midpoint(D, F) → M
  6. Rotate(D, 90*°, M) → D'
  7. Line(D', p) → g_1
  8. Segment(C, D) → r
  9. Intersect(g_1, r) → P
  10. Mirror(P, D') → P'
  11. Segment(D', P') → k_1
  12. Midpoint(B, A) → I
  13. Midpoint(B, I) → J
  14. Line(J, p) → s
  15. Intersect(r, s) → G
  16. Midpoint(G, J) → N
  17. Segment(N, J) → i_1
  18. Line(B, yAxis) → e
  19. Line(A, yAxis) → f
  20. Segment(C, B) → j
  21. Point(j) → E
  22. Polygon(E, B, A) → poly1, a_1, e_1, b_1
  23. Polygon(F, B, A) → poly2, a_2, f_1, b_2
  24. Angle(A, B, F) → α
  25. Angle(B, F, A) → β
  26. Angle(B, E, A) → γ
  27. Angle(E, A, B) → δ
  28. Angle(A, B, E) → ε
  29. Angle(F, A, B) → ζ
  30. Segment(D, A) → q
  31. Midpoint(I, A) → K
  32. Line(K, s) → t
  33. Intersect(r, t) → H
  34. Segment(G, J) → c_1
  35. Point(i_1) → L
  36. Polygon(L, A, D) → poly3, d_1, l_1, a_3
  37. Angle(L, D, A) → η
  38. Angle(D, A, L) → θ
  39. Segment(P, P') → h_1
  40. Point(k_1) → Q
  41. Polygon(Q, D, F) → poly4, f_2, q_1, d_2
  42. Angle(Q, D, A) → ι
  43. Angle(D, A, Q) → κ
  44. Segment(D', Q) → j_1
  45. Midpoint(H, K) → S
  46. Segment(S, K) → m_1
  47. Point(m_1) → T
  48. Polygon(C, T, B) → poly5, b_3, c_2, t_1
  49. Angle(B, C, T) → λ
  50. Angle(T, B, C) → μ
  51. Midpoint(S, M) → U
  52. Midpoint(K, A) → V
  53. Segment(U, V) → n_1
  54. Point(n_1) → W
  55. Polygon(C, W, B) → poly6, b_4, c_3, w
  56. Angle(W, B, C) → ν
  57. Angle(B, C, W) → ξ
  58. Segment(L, A) → p_1
  59. Segment(A, D) → r_1
  60. Segment(L, D) → s_1
  61. Segment(L, A) → e_2
  62. Segment(L, D) → g_2
  63. Segment(A, D) → h_2
  64. Segment(C, T) → i_2
  65. Segment(T, B) → j_2
  66. Segment(C, B) → k_2
  67. Segment(C, T) → l_2
  68. Segment(T, B) → m_2
  69. Segment(C, B) → n_2
  70. Segment(Q, D) → p_2
  71. Segment(D, F) → q_2
  72. Segment(Q, F) → r_2
  73. Segment(Q, D) → s_2
  74. Segment(D, F) → t_2
  75. Segment(Q, F) → d_3
  76. Segment(C, W) → e_3
  77. Segment(W, B) → f_3
  78. Segment(C, B) → g_3
  79. Segment(C, W) → h_3
  80. Segment(W, B) → i_3
  81. Segment(C, B) → j_3
  82. Textfield(text1) → inputBox1
  83. Textfield(Work) → inputBox2
  84. Line(A, L) → k_3
  85. OrthogonalLine(L, k_3) → l_3
  86. Point(l_3) → Z
  87. Element(answer, Problem) → m_3
  88. Angle(A, L, D) → ο
  89. Angle(A, L, D) → ρ
  90. Angle(A, L, D) → σ
  91. Angle(F, Q, D) → τ
  92. Angle(F, Q, D) → υ
  93. Angle(F, Q, D) → ϕ
  94. Angle(C, T, B) → χ
  95. Angle(C, T, B) → ψ
  96. Angle(C, T, B) → ω
  97. Angle(C, W, B) → α_1
  98. Angle(C, W, B) → β_1
  99. Angle(C, W, B) → γ_1
  100. Element(angle, Problem) → δ_1
  101. LaTeX(right, true, true) → text3
  102. LaTeX(wrong, true, true) → text4
  103. Textfield(Name) → inputBox3
  104. Textfield(Date) → inputBox4
  105. Segment(C_1, D_1) → n_3
  106. Point(n_3) → E_1
  107. Ellipse(A_1, B_1, E_1) → p_3
  108. Mirror(B, A) → B'
  109. Ellipse(C, B', E_1) → q_3
  110. Point(q_3) → F_1
  111. Point(q_3) → G_1

AI 绘图提示语参考

画一个包含30°-60°-90°和45°-45°-90°特殊直角三角形的几何图形,展示它们的构造和性质。首先画出两个直角三角形,然后通过旋转、镜像和连接等操作构造出新的图形。标注关键点、线段和中点,并显示角度和文本信息,帮助理解三角形的边长比和角度关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。