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四边形面积与中位线演示

四边形面积与中位线演示
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2014-03-30 13:45
向量几何作图
所属专题 Phebe Tanner Translation Tessallation
①本范例演示了如何通过动态演示四边形的面积和中位线性质；②涉及核心数学概念包括四边形、面积计算、中位线定理、向量运算；③作图要点使用了Line, OrthogonalLine, Point, Intersect, Segment, Angle, Vector, Translate, Polygon等GeoGebra命令和对象；④适合高中数学教学，用于理解四边形几何性质和向量应用。

GeoGebra 命令及参数

  1. Line(A, B) → a
  2. OrthogonalLine(B, a) → b
  3. OrthogonalLine(A, a) → c
  4. Point(b) → C
  5. OrthogonalLine(C, c) → d
  6. Intersect(c, d) → D
  7. Segment(D, C) → e
  8. Segment(C, B) → f
  9. Segment(B, A) → g
  10. Segment(A, D) → h
  11. Angle(A, B, C) → α
  12. Angle(C, D, A) → β
  13. Angle(D, A, B) → γ
  14. Angle(B, C, D) → δ
  15. Segment(D, E) → i
  16. Segment(E, F) → j
  17. Segment(F, G) → k
  18. Segment(G, H) → l
  19. Segment(H, I) → m
  20. Segment(I, J) → n
  21. Segment(J, K) → p
  22. Segment(K, L) → q
  23. Segment(L, M) → r
  24. Segment(M, C) → s
  25. Vector(C, B) → u
  26. Translate(D, u) → D'
  27. Translate(E, u) → E'
  28. Segment(D', E') → i'
  29. Translate(E, u) → E'_1
  30. Translate(F, u) → F'
  31. Segment(E'_1, F') → j'
  32. Translate(F, u) → F'_1
  33. Translate(G, u) → G'
  34. Segment(F'_1, G') → k'
  35. Translate(G, u) → G'_1
  36. Translate(H, u) → H'
  37. Segment(G'_1, H') → l'
  38. Translate(H, u) → H'_1
  39. Translate(I, u) → I'
  40. Segment(H'_1, I') → m'
  41. Translate(I, u) → I'_1
  42. Translate(J, u) → J'
  43. Segment(I'_1, J') → n'
  44. Translate(J, u) → J'_1
  45. Translate(K, u) → K'
  46. Segment(J'_1, K') → p'
  47. Translate(K, u) → K'_1
  48. Translate(L, u) → L'
  49. Segment(K'_1, L') → q'
  50. Translate(L, u) → L'_1
  51. Translate(M, u) → M'
  52. Segment(L'_1, M') → r'
  53. Translate(M, u) → M'_1
  54. Translate(C, u) → C'
  55. Segment(M'_1, C') → s'
  56. Segment(D, N) → t
  57. Segment(N, O) → a_1
  58. Segment(O, P) → b_1
  59. Segment(P, Q) → c_1
  60. Segment(Q, R) → d_1
  61. Segment(R, S) → e_1
  62. Segment(S, T) → f_1
  63. Segment(T, U) → g_1
  64. Segment(U, V) → h_1
  65. Segment(V, W) → i_1
  66. Segment(W, Z) → j_1
  67. Segment(Z, A) → k_1
  68. Vector(A, B) → v
  69. Translate(D, v) → D'_1
  70. Translate(N, v) → N'
  71. Segment(D'_1, N') → t'
  72. Translate(N, v) → N'_1
  73. Translate(O, v) → O'
  74. Segment(N'_1, O') → l_1
  75. Translate(O, v) → O'_1
  76. Translate(P, v) → P'
  77. Segment(O'_1, P') → m_1
  78. Translate(P, v) → P'_1
  79. Translate(Q, v) → Q'
  80. Segment(P'_1, Q') → n_1
  81. Translate(Q, v) → Q'_1
  82. Translate(R, v) → R'
  83. Segment(Q'_1, R') → p_1
  84. Translate(R, v) → R'_1
  85. Translate(S, v) → S'
  86. Segment(R'_1, S') → q_1
  87. Translate(S, v) → S'_1
  88. Translate(T, v) → T'
  89. Segment(S'_1, T') → r_1
  90. Translate(T, v) → T'_1
  91. Translate(U, v) → U'
  92. Segment(T'_1, U') → s_1
  93. Translate(U, v) → U'_1
  94. Translate(V, v) → V'
  95. Segment(U'_1, V') → t_1
  96. Translate(V, v) → V'_1
  97. Translate(W, v) → W'
  98. Segment(V'_1, W') → a_2
  99. Translate(W, v) → W'_1
  100. Translate(Z, v) → Z'
  101. Segment(W'_1, Z') → b_2
  102. Translate(Z, v) → Z'_1
  103. Translate(A, v) → A'
  104. Segment(Z'_1, A') → c_2
  105. Translate(D', v) → D''
  106. Intersect(j_1, k_1) → A_1
  107. Point(i_1) → B_1
  108. Intersect(h_1, i_1) → C_1
  109. Intersect(g_1, h_1) → D_1
  110. Intersect(f_1, g_1) → E_1
  111. Point(e_1) → F_1
  112. Intersect(d_1, e_1) → G_1
  113. Intersect(c_1, d_1) → H_1
  114. Intersect(b_1, c_1) → I_1
  115. Intersect(t, a_1) → J_1
  116. Intersect(i, t) → K_1
  117. Intersect(i, j) → L_1
  118. Intersect(i', k_1) → M_1
  119. Intersect(j_1, k_1) → N_1
  120. Intersect(i_1, j_1) → O_1
  121. Point(i_1) → P_1
  122. Intersect(g_1, h_1) → Q_1
  123. Intersect(f_1, g_1) → R_1
  124. Intersect(d_1, e_1) → S_1
  125. Intersect(c_1, d_1) → T_1
  126. Intersect(b_1, c_1) → U_1
  127. Intersect(t, a_1) → V_1
  128. Intersect(i, t) → W_1
  129. Intersect(i, j) → Z_1
  130. Intersect(j, k) → A_2
  131. Intersect(k, l) → B_2
  132. Intersect(l, m) → C_2
  133. Intersect(m, n) → D_2
  134. Intersect(n, p) → E_2
  135. Point(q) → F_2
  136. Intersect(r, s) → G_2
  137. Intersect(s, t') → H_2
  138. Intersect(t', l_1) → I_2
  139. Intersect(m_1, n_1) → J_2
  140. Intersect(n_1, p_1) → K_2
  141. Intersect(p_1, q_1) → L_2
  142. Intersect(q_1, r_1) → M_2
  143. Intersect(r_1, s_1) → N_2
  144. Intersect(s_1, t_1) → O_2
  145. Intersect(t_1, a_2) → P_2
  146. Intersect(a_2, b_2) → Q_2
  147. Intersect(b_2, c_2) → R_2
  148. Intersect(s', c_2) → S_2
  149. Intersect(r', s') → T_2
  150. Point(q') → U_2
  151. Intersect(n', p') → V_2
  152. Intersect(m', n') → W_2
  153. Intersect(l', m') → Z_2
  154. Point(l') → A_3
  155. Intersect(j', k') → B_3
  156. Intersect(i', j') → C_3
  157. Polygon(M_1, N_1, W_1, Z_1, A_2, B_2, C_2, D_2, E_2, F_2, G_2, H_2, O_1, I_2, J_2, K_2, L_2, M_2, N_2, O_2, P_2, Q_2, R_2, P_1, S_2, T_2, U_2, V_2, W_2, Z_2, A_3, B_3, C_3, Q_1, R_1, S_1, T_1, U_1, V_1) → poly1, m_2, v_1, w_1, z_1, a_3, b_3, c_3, d_2, e_2, f_2, g_2, n_2, h_2, i_2, j_2, k_2, l_2, m_3, n_3, o_2, p_3, q_3, o_1, r_3, s_3, t_3, u_2, v_2, w_2, z_2, a_4, b_4, c_4, p_2, q_2, r_2, s_2, t_2, u_1
  158. Segment(R_1, D_3) → d_3
  159. Segment(D_3, B_3) → e_3
  160. Polygon(D_3, R_1, C_2, D_2, E_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2, S_1, M_2, N_2, O_2, P_2, Q_2, R_2, S_2, T_2, U_2, V_2, T_1, W_2, Z_2, A_3, B_3, U_1, V_1, W_1, Z_1, A_2, B_2) → poly2, d_4, b_5, c_5, d_5, e_4, f_3, g_3, h_3, i_3, j_3, k_3, r_4, l_3, m_4, n_4, o_3, p_4, q_4, r_5, s_5, t_5, u_4, s_4, v_4, w_4, z_4, a_6, b_6, t_4, u_3, v_3, w_3, z_3, a_5
  161. Segment(M_1, O_1) → f_4
  162. Polygon(M_1, N_1, O_1) → poly3, o_4, m_5, n_5

AI 绘图提示语参考

绘制一个四边形ABCD，连接对角线AC和BD，找出它们的中点E和F，然后绘制四边形EFGH，其中E、F、G、H分别是AB、BC、CD、DA的中点。接着，画出四边形EFGH的对角线EG和FH，以及它们的中点I和J，最后连接I和J，形成线段IJ。
以上提示语为根据原始绘图命令整理而来，仅供参考。