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四边形乐园

四边形乐园
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2015-12-24 12:32
多边形变换几何作图
通过操作四边形，观察哪些特征会改变，哪些保持不变。本范例涉及四边形、平行四边形、矩形、菱形、正方形和梯形等核心概念。使用了线段、直线、交点、角、垂直线、点、圆、镜像等GeoGebra命令进行构造。适合初中及以上学生或教师使用。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. Segment(A, C) → b
  3. Line(B, b) → c
  4. Line(C, a) → d
  5. Intersect(c, d) → D
  6. Segment(B, D) → e
  7. Segment(C, D) → f
  8. Angle(B, A, C) → α
  9. Angle(C, D, B) → β
  10. Angle(D, B, A) → γ
  11. Angle(A, C, D) → δ
  12. Segment(E, F) → g
  13. Segment(E, G) → h
  14. Line(F, h) → i
  15. Line(G, g) → j
  16. Intersect(i, j) → H
  17. Segment(F, H) → k
  18. Segment(G, H) → l
  19. Segment(E, H) → m
  20. Segment(F, G) → n
  21. Intersect(m, n) → I
  22. Segment(E, I) → p
  23. Segment(I, H) → q
  24. Segment(F, I) → r
  25. Segment(I, G) → s
  26. Angle(I, E, G) → ε
  27. Angle(F, E, I) → ζ
  28. Angle(I, F, E) → η
  29. Angle(H, F, I) → θ
  30. Segment(J, K) → t
  31. OrthogonalLine(J, t) → a_1
  32. Point(a_1) → L
  33. Segment(J, L) → b_1
  34. OrthogonalLine(L, b_1) → c_1
  35. OrthogonalLine(K, t) → d_1
  36. Intersect(c_1, d_1) → M
  37. Segment(K, M) → e_1
  38. Segment(L, M) → f_1
  39. Angle(K, J, L) → ι
  40. Angle(J, L, M) → κ
  41. Angle(L, M, K) → λ
  42. Angle(M, K, J) → μ
  43. Segment(J, M) → g_1
  44. Segment(L, K) → h_1
  45. Intersect(g_1, h_1) → N
  46. Segment(J, N) → i_1
  47. Segment(N, M) → j_1
  48. Segment(L, N) → k_1
  49. Segment(N, K) → l_1
  50. Angle(N, J, L) → ν
  51. Angle(K, J, N) → ξ
  52. Angle(N, K, J) → ο
  53. Angle(M, K, N) → ρ
  54. Angle(G, I, E) → σ
  55. Angle(L, N, J) → τ
  56. Circle(O, P) → p_1
  57. Segment(P, O) → m_1
  58. Point(p_1) → Q
  59. Segment(O, Q) → n_1
  60. Line(Q, m_1) → q_1
  61. Line(P, n_1) → r_1
  62. Intersect(q_1, r_1) → R
  63. Segment(P, R) → s_1
  64. Segment(R, Q) → t_1
  65. Segment(O, R) → a_2
  66. Segment(Q, P) → b_2
  67. Intersect(a_2, b_2) → S
  68. Segment(O, S) → c_2
  69. Segment(S, R) → d_2
  70. Segment(Q, S) → e_2
  71. Segment(S, P) → f_2
  72. Angle(S, O, Q) → υ
  73. Angle(P, O, S) → ϕ
  74. Angle(S, P, O) → χ
  75. Angle(R, P, S) → ψ
  76. Angle(R, S, Q) → ω
  77. Circle(T, U) → g_2
  78. Segment(U, T) → h_2
  79. OrthogonalLine(T, h_2) → i_2
  80. Intersect(g_2, i_2, 1) → V
  81. Segment(T, V) → j_2
  82. Line(U, j_2) → k_2
  83. Line(V, h_2) → l_2
  84. Intersect(k_2, l_2) → W
  85. Segment(V, W) → m_2
  86. Segment(W, U) → n_2
  87. Angle(U, T, V) → α_1
  88. Angle(T, V, W) → β_1
  89. Angle(V, W, U) → γ_1
  90. Angle(W, U, T) → δ_1
  91. Segment(T, W) → p_2
  92. Segment(V, U) → q_2
  93. Intersect(p_2, q_2) → Z
  94. Segment(T, Z) → r_2
  95. Segment(Z, W) → s_2
  96. Segment(V, Z) → t_2
  97. Segment(Z, U) → a_3
  98. Angle(Z, T, V) → ε_1
  99. Angle(U, T, Z) → ζ_1
  100. Angle(Z, U, T) → η_1
  101. Angle(W, U, Z) → θ_1
  102. Angle(V, Z, T) → ι_1
  103. Circle(A_1, B_1) → c_3
  104. Segment(B_1, A_1) → b_3
  105. Point(c_3) → C_1
  106. Segment(A_1, C_1) → d_3
  107. Segment(B_1, C_1) → e_3
  108. OrthogonalLine(A_1, e_3) → f_3
  109. Point(f_3) → D_1
  110. Circle(D_1, B_1) → g_3
  111. Segment(B_1, D_1) → h_3
  112. Segment(D_1, C_1) → i_3
  113. Segment(A_1, D_1) → j_3
  114. Intersect(e_3, j_3) → E_1
  115. Segment(B_1, E_1) → k_3
  116. Segment(E_1, C_1) → l_3
  117. Segment(A_1, E_1) → m_3
  118. Segment(E_1, D_1) → n_3
  119. Angle(E_1, A_1, C_1) → κ_1
  120. Angle(B_1, A_1, E_1) → λ_1
  121. Angle(E_1, B_1, A_1) → μ_1
  122. Angle(D_1, B_1, E_1) → ν_1
  123. Angle(A_1, C_1, E_1) → ξ_1
  124. Angle(E_1, C_1, D_1) → ο_1
  125. Angle(C_1, D_1, E_1) → ρ_1
  126. Angle(E_1, D_1, B_1) → σ_1
  127. Angle(C_1, E_1, A_1) → τ_1
  128. Segment(F_1, G_1) → p_3
  129. Line(H_1, p_3) → q_3
  130. Point(q_3) → I_1
  131. Segment(H_1, I_1) → r_3
  132. Segment(F_1, H_1) → s_3
  133. Segment(G_1, I_1) → t_3
  134. Segment(F_1, I_1) → a_4
  135. Segment(G_1, H_1) → b_4
  136. Intersect(a_4, b_4) → J_1
  137. Segment(F_1, J_1) → c_4
  138. Segment(J_1, I_1) → d_4
  139. Segment(G_1, J_1) → e_4
  140. Segment(J_1, H_1) → f_4
  141. Angle(J_1, F_1, G_1) → υ_1
  142. Angle(H_1, F_1, J_1) → ϕ_1
  143. Angle(J_1, H_1, F_1) → χ_1
  144. Angle(I_1, H_1, G_1) → ψ_1
  145. Angle(G_1, J_1, F_1) → ω_1
  146. Segment(K_1, L_1) → g_4
  147. Segment(L_1, M_1) → h_4
  148. OrthogonalLine(M_1, h_4) → i_4
  149. Mirror(L_1, i_4) → N_1
  150. Mirror(K_1, i_4) → O_1
  151. Segment(L_1, N_1) → j_4
  152. Segment(K_1, O_1) → k_4
  153. Segment(O_1, N_1) → l_4
  154. Segment(K_1, N_1) → m_4
  155. Segment(O_1, L_1) → n_4
  156. Intersect(m_4, n_4) → P_1
  157. Segment(K_1, P_1) → p_4
  158. Segment(P_1, N_1) → q_4
  159. Segment(L_1, P_1) → r_4
  160. Segment(P_1, O_1) → s_4
  161. Angle(P_1, K_1, O_1) → α_2
  162. Angle(L_1, K_1, P_1) → β_2
  163. Angle(P_1, L_1, K_1) → γ_2
  164. Angle(N_1, L_1, P_1) → δ_2
  165. Angle(K_1, O_1, P_1) → ε_2
  166. Angle(P_1, O_1, N_1) → ζ_2
  167. Angle(O_1, N_1, P_1) → η_2
  168. Angle(P_1, N_1, L_1) → θ_2
  169. Angle(O_1, P_1, K_1) → ι_2