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Quadrilateral Area and Median Line Demonstration

Quadrilateral Area and Median Line Demonstration
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2014-03-30 13:45
VectorGeometric Construction
In collections Phebe Tanner Translation Tessallation
This example demonstrates how to dynamically visualize the area of a quadrilateral and the properties of its median line. It involves core mathematical concepts such as quadrilaterals, area calculation, median line theorem, and vector operations. The construction uses GeoGebra commands and objects like Line, OrthogonalLine, Point, Intersect, Segment, Angle, Vector, Translate, Polygon. Suitable for high school mathematics teaching to understand quadrilateral geometric properties and vector applications.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a quadrilateral ABCD, connect its diagonals AC and BD to find their midpoints E and F. Then, draw quadrilateral EFGH where E, F, G, and H are the midpoints of AB, BC, CD, and DA respectively. Next, draw the diagonals EG and FH of quadrilateral EFGH and their midpoints I and J. Finally, connect I and J to form segment IJ.
The prompt above was compiled from the original drawing commands and is for reference only.