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等腰三角形示例与反例：几何作图与性质分析

等腰三角形示例与反例：几何作图与性质分析
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2015-07-17 06:37
测试改名0角几何作图
本范例通过GeoGebra演示等腰三角形的构造与性质。核心数学概念包括三角形分类、角平分线、等腰三角形性质等。作图要点涉及使用Rotate、Angle、Segment、Point等命令，以及Midpoint、Circle等工具。适合初中生学习几何作图，或用于教学演示。

GeoGebra 命令及参数

  1. Rotate(A, 36*°, B) → A'
  2. Angle(A, B, A') → α
  3. Segment(C, D) → a
  4. Rotate(C, α, D) → C'
  5. Rotate(D, α, D) → D'
  6. Segment(C', D') → a'
  7. Point(a') → E
  8. Ray(D, E) → b
  9. Point(b) → F
  10. Segment(C, F) → c
  11. AngularBisector(C, D, F) → d
  12. Intersect(d, c) → G
  13. Segment(D, G) → e
  14. Segment(D, F) → f
  15. Angle(C, D, G) → β
  16. Angle(G, D, F) → γ
  17. Segment(H, I) → g
  18. Segment(H, J) → h
  19. Mirror(H, g) → H'
  20. Mirror(J, g) → J'
  21. Segment(H', J') → h'
  22. Segment(J, J') → i
  23. Angle(J', J, H) → δ
  24. Angle(H, J', J) → ε
  25. Segment(K, L) → j
  26. Segment(L, M) → k
  27. Segment(M, K) → l
  28. OrthogonalLine(L, l) → m
  29. Intersect(m, l) → N
  30. Segment(L, N) → n
  31. Angle(M, N, L) → ζ
  32. Point(Circle[O, 2.5]) → P
  33. Segment(O, P) → p
  34. Midpoint(O, P) → Q
  35. Segment(O, R) → q
  36. Segment(R, P) → r
  37. Segment(R, Q) → s
  38. Segment(S, T) → t
  39. Midpoint(S, T) → U
  40. OrthogonalLine(U, t) → a_1
  41. Point(a_1) → V
  42. Segment(S, V) → b_1
  43. Segment(V, T) → c_1
  44. Segment(V, U) → d_1
  45. Segment(W, Z) → e_1
  46. Midpoint(e_1) → A_1
  47. OrthogonalLine(A_1, e_1) → f_1
  48. Point(f_1) → B_1
  49. Segment(W, B_1) → g_1
  50. Segment(B_1, Z) → h_1
  51. Point(f_1) → C_1
  52. Point(f_1) → D_1
  53. Segment(C_1, D_1) → i_1
  54. Segment(E_1, F_1) → j_1
  55. Circle(G_1, 0.3) → k_1
  56. Midpoint(S, U) → H_1
  57. Point(k_1) → J_1
  58. Segment(G_1, J_1) → l_1
  59. Circle(H_1, l_1) → p_1
  60. OrthogonalLine(H_1, t) → m_1
  61. Intersect(p_1, m_1, 2) → K_1
  62. Intersect(p_1, m_1, 1) → L_1
  63. Segment(S, U) → q_1
  64. Segment(U, T) → r_1
  65. Midpoint(F_1, E_1) → I_1
  66. OrthogonalLine(I_1, j_1) → n_1
  67. Segment(F_1, I_1) → s_1
  68. Segment(I_1, E_1) → t_1
  69. Segment(E_1, M_1) → a_2
  70. Segment(M_1, F_1) → b_2
  71. Point(n_1) → N_1
  72. Point(n_1) → O_1
  73. Segment(N_1, O_1) → c_2
  74. Angle(F_1, I_1, O_1) → η
  75. Rotate(A_2, 36*°, B_2) → A'_1
  76. Angle(A_2, B_2, A'_1) → α_1
  77. Segment(C_2, D_2) → a_3
  78. Rotate(C_2, α_1, D_2) → C'_1
  79. Rotate(D_2, α_1, D_2) → D'_1
  80. Segment(C'_1, D'_1) → a'_1
  81. Point(a'_1) → E_2
  82. Ray(D_2, E_2) → b_3
  83. Point(b_3) → F_2
  84. Segment(C_2, F_2) → c_3
  85. AngularBisector(C_2, D_2, F_2) → d_2
  86. Intersect(d_2, c_3) → G_2
  87. Segment(D_2, G_2) → e_2
  88. Segment(D_2, F_2) → f_2
  89. Angle(C_2, D_2, G_2) → β_1
  90. Angle(G_2, D_2, F_2) → γ_1
  91. OrthogonalLine(C_2, e_2) → g_2
  92. Intersect(g_2, f_2) → P_1
  93. Segment(D_2, P_1) → h_2
  94. Midpoint(C_2, P_1) → Q_1
  95. Segment(C_2, P_1) → i_2
  96. Segment(Q_1, D_2) → j_2
  97. Angle(P_1, Q_1, D_2) → θ
  98. Angle(T, U, V) → ι