积极 AI Logo 积极 AI

平行四边形中的几何问题

平行四边形中的几何问题
几何画板及绘图内容加载中，请稍等……
2017-09-13 18:54
多边形变换几何作图
这是一个动态可修改的平行四边形问题示例。通过旋转、平移等几何变换，可以探索平行四边形中的各种几何关系。使用了Line, Ray, Rotate, Point, Midpoint, Intersect, Segment, Angle, Min, Circle, Dilate, CircleSector, Vector, Translate, Polygon, LineBisector, Distance等GeoGebra命令。适合初中及以上学生学习几何变换和探索平行四边形的性质。

GeoGebra 命令及参数

  1. Line(A, B) → s_1
  2. Ray(A, B) → f
  3. Rotate(B, a°, A) → B'
  4. Ray(A, B') → g
  5. Point(g) → C
  6. Midpoint(B, C) → W
  7. Line(W, s_1) → t_1
  8. Line(C, f) → i
  9. Line(B, g) → h
  10. Intersect(h, i) → D
  11. Segment(D, B) → k_1
  12. Intersect(t_1, k_1) → F_1
  13. Segment(D, F_1) → k_2
  14. Angle(B, A, B') → α
  15. Segment(C, D) → j
  16. Segment(A, B) → k
  17. Segment(B, D) → l
  18. Segment(A, C) → m
  19. Min(m, k) → b
  20. Circle(C, (0.2 * b)) → d
  21. Circle(A, (0.15 * b)) → e
  22. Circle(B, (0.2 * b)) → p
  23. Circle(D, (0.2 * b)) → c
  24. Intersect(e, k, 1) → E
  25. Intersect(e, m, 1) → F
  26. Intersect(p, k, 1) → G
  27. Intersect(p, l, 1) → H
  28. Intersect(d, g, 2) → I
  29. Ray(C, I) → q
  30. Intersect(c, h, 2) → J
  31. Ray(D, J) → r
  32. Intersect(c, i, 2) → K
  33. Ray(D, K) → s
  34. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'
  35. Segment(A, A') → t
  36. Rotate(E, If[1 < o ≤ 2, ((o - 1) * α), α], A) → E'
  37. CircleSector(A, E, E') → c_1
  38. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], C) → A'_1
  39. Vector(A, A'_1) → u
  40. Translate(c_1, u) → d_1
  41. Segment(A, A'_1) → f_1
  42. Dilate(C, If[3 < o ≤ 4, 4 - o, 0], D) → C'
  43. Vector(C, C') → v
  44. Translate(d_1, v) → e_1
  45. Segment(C, C') → g_1
  46. Dilate(D, If[4 < o ≤ 5, 5 - o, 0], B) → D'
  47. Segment(D, D') → h_1
  48. Polygon(A, B, D, C) → poly1, a_1, b_1, d_2, c_2
  49. Dilate(A, If[5.5 < o ≤ 6.5, 6.5 - o, 0], C) → A'_2
  50. Vector(A, A'_2) → w
  51. Translate(A, w) → A'_3
  52. Translate(A', w) → A''
  53. Dilate(A, If[6.5 < o ≤ 7.5, 7.5 - o, 0], B) → A'_4
  54. Vector(A, A'_4) → u_1
  55. Translate(A, u_1) → A'_5
  56. Translate(A'_1, u_1) → L
  57. Intersect(d, i) → M, N
  58. Intersect(d, g) → O, P
  59. Angle(A, C, N) → β
  60. Rotate(N, If[6.5 < o ≤ 7.5, ((-(o - 6.5)) * β), (-β)], C) → N'
  61. Dilate(C, If[7.5 < o ≤ 8.5, 8.5 - o, 0], B) → C'_1
  62. Vector(C, C'_1) → v_1
  63. Ray(A, B) → q_1
  64. LineBisector(B, A) → r_1
  65. Distance(C, B) → distanceCB
  66. Segment(C, D) → i_1
  67. Line(A, D) → j_1
  68. Line(C, A) → m_1
  69. Intersect(e, j_1) → S, T
  70. Intersect(e, m_1) → U, V
  71. Angle(D, A, C) → γ
  72. Rotate(T, If[10 < o ≤ 11, ((o - 10) * γ), γ], A) → T'
  73. Midpoint(A, D) → A_1
  74. Midpoint(C, D) → Q
  75. Midpoint(A, B) → R
  76. Point(k_2) → Z
  77. Ray(Z, Q) → l_1
  78. Ray(B, C) → n_1
  79. Intersect(n_1, l_1) → B_1
  80. Ray(R, B_1) → p_1
  81. Intersect(t_1, p_1) → C_1
  82. Line(C_1, Q) → f_2
  83. Line(R, Z) → g_2
  84. Line(C, A) → h_2
  85. Intersect(h_2, t_1) → D_1
  86. Intersect(n_1, l_1) → E_1
  87. Segment(R, C_1) → i_2
  88. Dilate(A, If[6 < o ≤ 7, 7 - o, 0], R) → A'_6
  89. Segment(A, A'_6) → l_2
  90. Rotate(A, If[7 < o ≤ 8, ((-(o - 7)) * π), (-π)], R) → A'_7
  91. Rotate(A'_6, If[7 < o ≤ 8, ((-(o - 7)) * π), (-π)], R) → G_1
  92. Segment(A'_7, G_1) → m_2
  93. Dilate(A, If[8 < o ≤ 9, 9 - o, 0], C) → A'_8
  94. Vector(A, A'_8) → w_1
  95. Translate(A, w_1) → A'_9
  96. Translate(A'_6, w_1) → H_1
  97. Segment(A'_9, H_1) → n_2
  98. Translate(A'_7, w_1) → L_1
  99. Translate(G_1, w_1) → M_1
  100. Segment(L_1, M_1) → p_2
  101. Dilate(B, If[9 < o ≤ 10, 10 - o, 0], W) → B'_1
  102. Segment(B, B'_1) → j_2
  103. Dilate(W, If[10 < o ≤ 11, 11 - o, 0], C) → W'
  104. Segment(W, W') → q_2
  105. Rotate(B, If[11 < o ≤ 12, ((-(o - 11)) * π), (-π)], W) → B'_2
  106. Rotate(B'_1, If[11 < o ≤ 12, ((-(o - 11)) * π), (-π)], W) → I_1
  107. Segment(B'_2, I_1) → r_2
  108. Dilate(Z, If[13 < o ≤ 14, 14 - o, 0], Q) → Z'
  109. Segment(Z, Z') → s_2
  110. Dilate(Q, If[14 < o ≤ 15, 15 - o, 0], B_1) → Q'
  111. Segment(Q, Q') → t_2
  112. Dilate(C, If[14 < o ≤ 15, 15 - o, 0], B_1) → C'_2
  113. Segment(C, C'_2) → a_2
  114. Dilate(W, If[15 < o ≤ 16, 16 - o, 0], D_1) → W'_1
  115. Segment(W, W'_1) → b_2
  116. Line(W, D_1) → e_2
  117. Circle(D_1, 2) → c_3
  118. Intersect(c_3, e_2) → J_1, K_1
  119. Ray(D_1, K_1) → f_3
  120. Rotate(d_1, If[16 < o ≤ 17, ((o - 16) * π), π], C) → d_3
  121. Dilate(C, If[17 < o ≤ 18, 18 - o, 0], D_1) → C'_3
  122. Vector(C, C'_3) → u_2
  123. Translate(d_3, u_2) → e_3
  124. Intersect(g_2, j_2) → N_1
  125. Segment(R, N_1) → g_3
  126. Min(i_2, g_3) → o_1
  127. Circle(R, (0.35 * o_1)) → h_3
  128. Intersect(h_3, g_2) → O_1, P_1
  129. Angle(N_1, R, C_1) → δ
  130. Dilate(B_1, If[18 < o ≤ 19, 19 - o, 0], C_1) → Q_1
  131. Segment(B_1, Q_1) → i_3
  132. Dilate(C_1, If[19 < o ≤ 20, 20 - o, 0], R) → R_1
  133. Segment(C_1, R_1) → j_3
  134. Dilate(R, If[20 < o ≤ 21, 21 - o, 0], Z) → R'
  135. Segment(R, R') → k_3
  136. Dilate(C_1, If[21 < o ≤ 22, 22 - o, 0], Q) → S_1
  137. Segment(C_1, S_1) → l_3
  138. Rotate(P_1, If[22 < o ≤ 23, ((o - 22) * δ), δ], R) → T_1
  139. CircleSector(R, P_1, T_1) → p_3
  140. Dilate(R, If[23 < o ≤ 24, 24 - o, 0], C_1) → R'_1
  141. Vector(R, R'_1) → v_2
  142. Translate(p_3, v_2) → q_3

AI 绘图提示语参考

绘制一个平行四边形ABCD，其中A、B、C、D是顶点。首先画出AB和BC的中点W，然后通过W画一条直线t1与AB平行。接着画出从C到f的直线i，与h相交于D。连接BD，然后在BD上取点F1，使得DF1平行于t1。接着画出角BAC的度数为α，然后画出以C、D为圆心，以BD长度的0.2倍为半径的圆c、p、d，与相应直线相交得到E、F、G、H。然后画出以A为圆心，以BD长度的0.15倍为半径的圆e，与相应直线相交得到E'，再画出以A为圆心，E'E为半径的扇形c1。接着画出以C为圆心，以BD长度的0.2倍为半径的圆p，与相应直线相交得到C'，再画出以C为圆心，C'C为半径的圆e1。最后画出以D为圆心，以BD长度的0.2倍为半径的圆p，与相应直线相交得到D'，再画出以D为圆心，D'D为半径的圆d1。
以上提示语为根据原始绘图命令整理而来，仅供参考。