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Mother Line Construction

Mother Line Construction
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2014-02-14 01:12
TriangleAngleGeometric Construction
This applet demonstrates the mother line phenomenon discovered through folding activities. Key mathematical concepts include similar triangles and angle bisectors. Using GeoGebra commands such as Polygon, Point, Segment, and AngularBisector, complex geometric shapes can be constructed. Suitable for geometry construction demonstrations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → veelhoek1, a, b, c, d, C, D
  2. Polygon(I, J, 4) → veelhoek3, i, j, k, l, K, L
  3. Point(d) → Q
  4. Point(b) → R
  5. Segment(Q, R) → r
  6. Point(k) → U
  7. Point(j) → V
  8. Segment(U, V) → t
  9. AngularBisector(d, r) → b_1, c_1
  10. AngularBisector(r, b) → d_1, e_1
  11. AngularBisector(r, a) → f_1, g_1
  12. AngularBisector(c, r) → h_1, i_1
  13. Intersect(e_1, c) → A_1
  14. Segment(A_1, R) → j_1
  15. Intersect(i_1, d) → B_1
  16. Intersect(i_1, b) → C_1
  17. Segment(B_1, C_1) → k_1
  18. Intersect(c_1, c) → D_1
  19. Segment(Q, D_1) → l_1
  20. Intersect(b_1, a) → E_1
  21. Segment(Q, E_1) → m_1
  22. Intersect(d_1, a) → F_1
  23. Segment(F_1, R) → n_1
  24. Intersect(f_1, d) → G_1
  25. Intersect(f_1, b) → H_1
  26. Segment(G_1, H_1) → p_1
  27. Intersect(j_1, l_1) → I_1
  28. Intersect(j_1, k_1) → J_1
  29. Intersect(k_1, l_1) → K_1
  30. Intersect(m_1, p_1) → L_1
  31. Intersect(n_1, p_1) → M_1
  32. Intersect(m_1, n_1) → N_1
  33. AngularBisector(t, k) → e, f
  34. AngularBisector(t, j) → g, h
  35. AngularBisector(t, l) → s, q_1
  36. AngularBisector(t, i) → r_1, s_1
  37. Intersect(s, k) → G
  38. Intersect(s, i) → H
  39. Segment(G, H) → t_1
  40. Intersect(g, i) → S
  41. Segment(S, V) → a_2
  42. Intersect(e, l) → T
  43. Segment(T, U) → b_2
  44. Intersect(f, j) → O_1
  45. Segment(U, O_1) → c_2
  46. Intersect(h, k) → P_1
  47. Segment(P_1, V) → d_2
  48. Intersect(r_1, l) → Q_1
  49. Intersect(r_1, j) → R_1
  50. Segment(Q_1, R_1) → e_2
  51. Intersect(g, l) → S_1
  52. Segment(S_1, V) → f_2
  53. Intersect(e, i) → T_1
  54. Segment(U, T_1) → g_2
  55. Intersect(t_1, g_2) → U_1
  56. Intersect(e_2, g_2) → V_1
  57. Intersect(f_2, g_2) → W_1
  58. Intersect(t_1, f_2) → Z_1
  59. Intersect(e_2, f_2) → A_2
  60. Intersect(c_2, d_2) → B_2
  61. Intersect(b_2, e_2) → C_2
  62. Intersect(t_1, b_2) → D_2
  63. Intersect(t_1, e_2) → E_2
  64. Intersect(t_1, a_2) → F_2
  65. Intersect(a_2, e_2) → G_2
  66. Point(c) → H_2
  67. Point(a) → I_2
  68. Segment(H_2, I_2) → h_2
  69. Point(d) → J_2
  70. Point(b) → K_2
  71. Segment(J_2, K_2) → i_2
  72. Intersect(b, c) → L_2
  73. Intersect(a, d) → M_2
  74. Segment(L_2, M_2) → j_2
  75. Point(k) → N_2
  76. Point(l) → P_2
  77. Point(j) → Q_2
  78. Segment(P_2, Q_2) → l_2
  79. Intersect(k, l) → R_2
  80. Intersect(i, j) → S_2
  81. Segment(R_2, S_2) → m_2
  82. Intersect(j, k) → T_2
  83. Intersect(i, l) → U_2
  84. Segment(T_2, U_2) → n_2
  85. Intersect(c, d) → V_2
  86. Intersect(a, b) → W_2
  87. Segment(V_2, W_2) → p_2
  88. Intersect(i, l) → Z_2
  89. Intersect(k, l) → A_3
  90. Ray(Z_2, A_3) → q_2
  91. Line(U, V) → r_2
  92. Intersect(i, j) → B_3
  93. Ray(Z_2, B_3) → s_2
  94. Intersect(r_2, q_2) → C_3
  95. Intersect(r_2, s_2) → O
  96. Segment(C_3, A_3) → m
  97. Segment(C_3, U) → n
  98. Segment(V, O) → p
  99. Segment(O, B_3) → q
  100. Segment(A_2, O) → a_1
  101. Segment(U_1, C_3) → t_2
  102. Intersect(j, e_2) → P
  103. Segment(P, O) → a_3
  104. Intersect(k, t_1) → W
  105. Segment(C_3, W) → b_3
  106. OrthogonalLine(E_2, t) → c_3
  107. Intersect(c_3, t) → Z
  108. Circle(E_2, Z) → d_3
  109. OrthogonalLine(B_2, t) → e_3
  110. Intersect(e_3, t) → D_3
  111. Circle(B_2, D_3) → f_3
  112. OrthogonalLine(U_1, t) → g_3
  113. Intersect(g_3, t) → E_3
  114. OrthogonalLine(U_1, l) → i_3
  115. Intersect(i_3, l) → F_3
  116. OrthogonalLine(D_2, k) → j_3
  117. Intersect(j_3, k) → G_3
  118. Ray(Q, R) → l_3
  119. Intersect(c, d) → H_3
  120. Intersect(b, c) → I_3
  121. Ray(H_3, I_3) → m_3
  122. Intersect(l_3, m_3) → J_3
  123. Segment(I_3, J_3) → n_3
  124. Segment(J_3, R) → p_3
  125. Intersect(b, k_1) → K_3
  126. Segment(K_3, J_3) → q_3
  127. OrthogonalLine(K_1, c) → r_3
  128. Intersect(r_3, c) → L_3
  129. Circle(K_1, L_3) → s_3
  130. Intersect(a, b) → M_3
  131. Intersect(a, d) → N_3
  132. Line(M_3, N_3) → t_3
  133. Line(R, Q) → a_4
  134. Intersect(t_3, a_4) → O_3
  135. Segment(O_3, Q) → b_4
  136. Segment(O_3, N_3) → c_4
  137. Intersect(d, p_1) → P_3
  138. Segment(O_3, P_3) → d_4
  139. OrthogonalLine(M_1, b) → e_4
  140. Intersect(e_4, b) → Q_3
  141. Circle(M_1, Q_3) → f_4
  142. OrthogonalLine(J_1, c) → g_4
  143. OrthogonalLine(L_1, a) → h_4
  144. Intersect(g_4, c) → R_3
  145. Intersect(h_4, a) → S_3
  146. Circle(J_1, R_3) → k_4
  147. Circle(L_1, S_3) → p_4
  148. OrthogonalLine(G_2, i) → i_4
  149. Intersect(i_4, i) → T_3
  150. Midpoint(k) → U_3
  151. Midpoint(i) → V_3
  152. Segment(U_3, V_3) → k_2
  153. OrthogonalLine(D_2, k) → h_3
  154. OrthogonalLine(G_2, i) → k_3
  155. Intersect(h_3, k) → W_3
  156. Intersect(k_3, i) → Z_3
  157. Circle(D_2, W_3) → q_4
  158. Circle(G_2, Z_3) → r_4
  159. OrthogonalLine(U_1, k) → j_4
  160. OrthogonalLine(A_2, i) → l_4
  161. Intersect(j_4, k) → A_4
  162. Intersect(l_4, i) → B_4
  163. Circle(U_1, A_4) → s_4
  164. Circle(A_2, B_4) → t_4

AI Drawing Prompt Reference

Draw a complex geometric figure composed of multiple triangles and segments. Start by drawing two quadrilaterals, then find the midpoints of their sides and diagonals to connect them with new segments. Use the angle bisector method to construct more segments and intersections from these segments, ultimately forming a complex figure made up of multiple triangles and segments.
The prompt above was compiled from the original drawing commands and is for reference only.