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等腰三角形示例与非示例 by Sergio lazo

等腰三角形示例与非示例 by Sergio lazo
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2015-10-16 00:55
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①本范例通过动态演示展示等腰三角形的定义及其与非等腰三角形的区别；②涉及核心概念包括等腰三角形的性质、角平分线、对称性、线性回归等；③构造过程中运用了旋转、角、线段、点、射线、角平分线、交点、镜像、垂线、中点、圆等 GeoGebra 命令与对象；④适合高中数学教学，用于加深学生对等腰三角形性质的理解和识别能力。

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