Quadrilateral Constructions by Taylor Rish

Quadrilateral Constructions by Taylor Rish
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2016-11-24 02:38
This example demonstrates methods for constructing quadrilaterals. Key mathematical concepts include geometric constructions, trigonometric functions, and transformations. Using GeoGebra commands such as Segment, Circle, and Intersect, various types of quadrilaterals can be constructed. Suitable for middle and high school students learning geometric constructions.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Circle(C, Segment[C, D]) → c
  3. Intersect(c, f, 1) → E
  4. Circle(E, Segment[C, D]) → d
  5. Intersect(d, f, 1) → F
  6. Circle(F, Segment[C, D]) → e
  7. Intersect(c, e, 1) → G
  8. Segment(C, G) → g
  9. Segment(G, F) → h
  10. Segment(E, C) → i
  11. Segment(F, E) → j
  12. Segment(E, F) → k
  13. Segment(E, F) → l
  14. Point(g) → H
  15. Point(h) → I
  16. Point(f) → J
  17. Point(i) → K
  18. Angle(K, C, H) → α
  19. Angle(H, G, I) → β
  20. Angle(I, F, J) → γ
  21. Angle(J, E, K) → δ
  22. Segment(G, E) → m
  23. Segment(C, F) → n
  24. Intersect(m, n) → L
  25. Angle(C, L, E) → ε
  26. Angle(F, L, G) → ζ
  27. Angle(G, L, C) → η
  28. Angle(E, L, F) → θ
  29. Segment(L, E) → p
  30. Segment(L, G) → q
  31. Segment(F, L) → r
  32. Segment(C, L) → s
  33. Segment(M, N) → t
  34. Segment(N, O) → a
  35. Point(t) → P
  36. Circle(N, Segment[N, P]) → c_1
  37. Intersect(c_1, a, 1) → Q
  38. Circle(Q, Segment[N, O]) → d_1
  39. Circle(P, Segment[O, N]) → e_1
  40. Circle(M, Segment[M, N]) → f_1
  41. Circle(N, Segment[N, M]) → g_1
  42. Point(g_1) → S
  43. Segment(N, S) → h_1
  44. Circle(S, Segment[M, N]) → k_1
  45. Intersect(f_1, k_1, 1) → T
  46. Segment(T, S) → i_1
  47. Segment(T, M) → j_1
  48. Angle(T, S, N) → ι
  49. Segment(S, N) → l_1
  50. Angle(S, N, P) → κ
  51. Angle(P, M, T) → λ
  52. Angle(M, T, S) → μ
  53. Segment(T, N) → b
  54. Segment(S, M) → m_1
  55. Intersect(b, m_1) → R
  56. Angle(T, R, M) → ν
  57. Angle(M, R, N) → ξ
  58. Angle(N, R, S) → ο
  59. Angle(S, R, T) → ρ
  60. Segment(T, R) → n_1
  61. Segment(R, N) → p_1
  62. Segment(S, R) → q_1
  63. Segment(R, M) → r_1
  64. Segment(U, V) → s_1
  65. Segment(U, W) → t_1
  66. Point(s_1) → Z
  67. Circle(U, Segment[Z, U]) → c_2
  68. Intersect(c_2, t_1, 1) → A_1
  69. Circle(Z, Segment[Z, A_1]) → d_2
  70. Circle(A_1, Segment[Z, A_1]) → e_2
  71. Intersect(d_2, e_2, 2) → B_1
  72. Segment(U, B_1) → a_1
  73. Segment(W, B_1) → b_1
  74. Segment(B_1, C_1) → f_2
  75. Segment(W, D_1) → g_2
  76. Intersect(f_2, g_2) → E_1
  77. Segment(W, E_1) → h_2
  78. Segment(E_1, B_1) → i_2
  79. Angle(U, W, E_1) → σ
  80. Angle(B_1, U, W) → τ
  81. Rotate(W, 90°, E_1) → W'
  82. Angle(W, E_1, W') → υ
  83. Rotate(E_1, 90°, B_1) → F_1
  84. Angle(E_1, B_1, F_1) → ϕ
  85. Segment(F_1, U) → j_2
  86. Segment(E_1, U) → k_2
  87. Intersect(b_1, k_2) → G_1
  88. Segment(H_1, I_1) → l_2
  89. Circle(I_1, Segment[H_1, I_1]) → p_2
  90. Circle(H_1, Segment[I_1, H_1]) → q_2
  91. Intersect(p_2, q_2, 2) → J_1
  92. Segment(J_1, K_1) → m_2
  93. Segment(J_1, H_1) → n_2
  94. Segment(H_1, K_1) → r_2
  95. Segment(J_1, I_1) → s_2
  96. Segment(I_1, K_1) → t_2
  97. Intersect(l_2, m_2) → L_1
  98. Angle(J_1, L_1, H_1) → χ
  99. Angle(I_1, L_1, J_1) → ψ
  100. Angle(K_1, L_1, I_1) → ω
  101. Angle(H_1, L_1, K_1) → α_1
  102. Angle(K_1, H_1, J_1) → β_1
  103. Angle(J_1, I_1, K_1) → γ_1
  104. Angle(L_1, K_1, H_1) → δ_1
  105. Angle(I_1, K_1, L_1) → ε_1
  106. Angle(H_1, J_1, L_1) → ζ_1
  107. Angle(L_1, J_1, I_1) → η_1
  108. Segment(M_1, N_1) → a_2
  109. Segment(O_1, P_1) → b_2
  110. Segment(P_1, N_1) → f_3
  111. Segment(O_1, M_1) → g_3
  112. Angle(M_1, O_1, P_1) → θ_1
  113. Angle(O_1, P_1, N_1) → ι_1
  114. Angle(N_1, M_1, O_1) → κ_1
  115. Angle(P_1, N_1, M_1) → λ_1
  116. Segment(O_1, N_1) → h_3
  117. Segment(M_1, P_1) → i_3
  118. Segment(Q_1, R_1) → j_3
  119. Line(S_1, j_3) → k_3
  120. Segment(Q_1, S_1) → l_3
  121. Line(R_1, l_3) → m_3
  122. Intersect(k_3, m_3) → T_1
  123. Segment(R_1, T_1) → n_3
  124. Segment(T_1, S_1) → p_3
  125. Angle(Q_1, R_1, T_1) → μ_1
  126. Angle(R_1, T_1, S_1) → ν_1
  127. Angle(T_1, S_1, Q_1) → ξ_1
  128. Angle(S_1, Q_1, R_1) → ο_1
  129. Segment(R_1, S_1) → q_3
  130. Segment(T_1, Q_1) → r_3
  131. Intersect(q_3, r_3) → U_1
  132. Segment(Q_1, U_1) → s_3
  133. Segment(U_1, T_1) → t_3
  134. Segment(R_1, U_1) → a_3
  135. Segment(U_1, S_1) → b_3

AI Drawing Prompt Reference

Construct a quadrilateral with points C and D as the endpoints of the diagonals. Use segments, circles, and intersections to determine the other vertices E, F, G, and H. Then, measure angles and connect segments to form the internal structure of the quadrilateral, including angles α, β, γ, and δ. Finally, use intersections of segments and circles to further refine the quadrilateral construction, ensuring all sides and angles meet geometric requirements.
The prompt above was compiled from the original drawing commands and is for reference only.