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菱形与正方形演示

菱形与正方形演示
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2018-03-27 00:35
多边形角解析几何变换几何作图
本范例演示了菱形与正方形的几何性质与相似变换。涉及的核心数学概念包括多边形、角度、相似变换和几何作图。构造过程中使用了Segment（线段）、Midpoint（中点）、OrthogonalLine（垂线）、Line（直线）、LineBisector（角平分线）、Intersect（交点）、Point（点）、Mirror（镜像）、Polygon（多边形）、Circle（圆）、TableText（表格文本）、Sum（求和）、Distance（距离）、InteriorAngles（内角）、Angle（角度）、PointIn（点在对象内）等GeoGebra命令和对象。适合初中及以上学生学习和理解几何变换与多边形性质。

GeoGebra 命令及参数

  1. Segment(A, B) → f
  2. Midpoint(f) → C
  3. Segment(C, B) → f_2
  4. OrthogonalLine(C, f_2) → f_3
  5. Line(M, O) → p
  6. Line(N, p) → q
  7. Segment(M, N) → m
  8. LineBisector(m) → n
  9. Intersect(n, p) → B_1
  10. OrthogonalLine(B_1, p) → j_1
  11. Intersect(q, j_1) → C_1
  12. Segment(D_1, E_1) → k_1
  13. Point(f_3) → D
  14. Segment(C, D) → g
  15. Mirror(C, C) → C'
  16. Mirror(D, C) → D'
  17. Segment(C', D') → g'
  18. Polygon(A, D, B, D') → poly1, a_1, d_1, b_1, d'
  19. Polygon(E, F, G, H) → poly2, e_1, f_1, g_1, h
  20. Segment(F, H) → i
  21. LineBisector(i) → j
  22. Intersect(j, h) → K
  23. Intersect(f_1, j) → L
  24. Segment(E, G) → k
  25. LineBisector(k) → l
  26. Intersect(l, h) → I
  27. Intersect(f_1, l) → J
  28. Segment(E, F) → r
  29. Point(p) → P
  30. Point(q) → Q
  31. Intersect(n, q) → R
  32. Polygon(M, R, N, P) → poly3, m_1, r_1, n_1, p_1
  33. Segment(Q, R) → s
  34. Point(k_1) → S
  35. Segment(Q, M) → t
  36. Point(Circle[S, s]) → T
  37. Segment(S, T) → h_1
  38. OrthogonalLine(S, h_1) → i_1
  39. Circle(S, t) → c_1
  40. Intersect(c_1, i_1) → U, V
  41. Polygon(S, U, T) → poly4, t_1, s_1, u
  42. Intersect(p, p_1) → W
  43. Intersect(p, poly3) → Z, A_1
  44. Polygon(M, R, C_1, B_1) → poly5, m_2, r_2, c_2, b_2
  45. Point(q) → F_1
  46. Polygon(Q, C_1, B_1, M) → poly6, q_1, c_3, b_3, m_3
  47. Polygon(M, R, N, B_1) → poly7, m_4, r_3, n_2, b_4
  48. Intersect(m_4, r_3) → G_1
  49. Intersect(r_3, n_2) → H_1
  50. Segment(A, C) → l_1
  51. Segment(I_1, J_1) → g_2
  52. Midpoint(g_2) → K_1
  53. OrthogonalLine(K_1, g_2) → h_2
  54. Point(h_2) → L_1
  55. Segment(L_1, K_1) → i_2
  56. Segment(I_1, K_1) → j_2
  57. Segment(K_1, J_1) → k_2
  58. Mirror(L_1, K_1) → M_1
  59. Mirror(K_1, K_1) → N_1
  60. Segment(M_1, N_1) → l_2
  61. Circle(K_1, J_1) → d_2
  62. OrthogonalLine(K_1, j_2) → p_2
  63. Intersect(d_2, p_2) → O_1, P_1
  64. Polygon(L_1, I_1, M_1, J_1) → poly8, l_3, i_3, m_5, j_3
  65. Polygon(Q_1, R_1, S_1, T_1) → poly9, q_2, r_4, s_2, t_2
  66. Segment(Q_1, S_1) → a_2
  67. Segment(R_1, T_1) → e_2
  68. Intersect(a_2, e_2) → U_1
  69. TableText({{A1, B1, C1, D1, E1}, {A2, B2, C2, D2, E2}, {A3, B3, C3, D3, E3}, {A4, B4, C4, D4, E4}, {A5, B5, C5, D5, E5}, {A6, B6, C6, D6, E6}, {A7, B7, C7, D7, E7}, {A8, B8, C8, D8, E8}}, "|_") → text4
  70. Sum(B2:B8) → B9
  71. Sum(C2:C8) → C9
  72. Sum(D2:D8) → D9
  73. Sum(E2:E8) → E9
  74. Sum(B9:E9) → F9
  75. Distance(a_1, l_1) → o
  76. InteriorAngles(poly1) → α, β, γ, δ
  77. InteriorAngles(poly1) → ε, ζ, η, θ
  78. Angle(C, C', A) → ι
  79. Angle(A, C, D') → κ
  80. Angle(B, C, D) → λ
  81. Angle(A, C, D) → μ
  82. Angle(D', C, B) → ν
  83. Distance(r_3, m_4) → v
  84. PointIn(poly7) → Pointpoly7
  85. Angle(L_1, K_1, J_1) → ξ
  86. Angle(M_1, K_1, J_1) → ο
  87. InteriorAngles(poly8) → ρ, σ, τ, υ
  88. Angle(I_1, K_1, M_1) → ϕ
  89. Angle(I_1, K_1, L_1) → χ
  90. Polygon(L_1, K_1, J_1) → t1, j_4, l_4, k_3
  91. Polygon(M_1, K_1, J_1) → t2, j_5, m_6, k_4
  92. Polygon(I_1, K_1, M_1) → t3, m_7, i_4, k_5
  93. Polygon(I_1, L_1, K_1) → t4, k_6, i_5, l_5