四边形及其对角线

四边形及其对角线
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2017-10-13 07:18
所属专题 Y7 Polygons
①本范例演示四边形的几何性质及其对角线的相关特性;②涉及的核心数学概念包括多边形、对角线、角、距离、几何作图等;③作图要点——从下方『构造摘要』提炼用到了 Line, Segment, Intersect, Distance, Circle, Point, OrthogonalLine, Mirror, Angle, Midpoint 等GeoGebra命令/对象;④适合高中阶段学习几何作图的学生或教师使用。

GeoGebra 命令及参数

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

AI 绘图提示语参考

绘制一个四边形ABCD,连接对角线AC和BD,标记它们的交点为E。然后以E为圆心,分别以A、B、C、D为圆周上的点画圆,标记圆的交点为F。接着画出四边形AEFD,连接对角线AF和DE,标记它们的交点为G。最后画出四边形AEGF,连接对角线AG和EF,标记它们的交点为H。
以上提示语为根据原始绘图命令整理而来,仅供参考。