Quadrilaterals and Diagonals

Quadrilaterals and Diagonals
Loading the math board and drawing, please wait…
2017-10-13 07:18
In collections Y7 Polygons
This example demonstrates the geometric properties of quadrilaterals and their diagonals. It involves core math concepts like polygons, diagonals, angles, distances, and geometric construction. The construction uses commands/objects such as Line, Segment, Intersect, Distance, Circle, Point, OrthogonalLine, Mirror, Angle, and Midpoint in GeoGebra. Suitable for high school students and teachers learning geometric constructions.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Line(C, a) → b
  3. Segment(C, A) → c
  4. Line(B, c) → d
  5. Segment(A, B) → e
  6. Intersect(b, d) → D
  7. Segment(C, D) → f
  8. Segment(D, B) → g
  9. Distance(A, B) → distanceAB
  10. Segment(C, B) → i
  11. Segment(A, D) → j
  12. Intersect(i, j) → E
  13. Circle(G, F) → k
  14. Segment(G, F) → l
  15. Point(k) → H
  16. Segment(G, H) → m
  17. Line(H, l) → n
  18. Line(F, m) → p
  19. Intersect(n, p) → I
  20. Segment(H, I) → q
  21. Segment(F, I) → r
  22. Segment(G, I) → s
  23. Segment(H, F) → t
  24. Intersect(s, t) → J
  25. Segment(K, L) → a_1
  26. OrthogonalLine(L, a_1) → b_1
  27. Point(b_1) → M
  28. OrthogonalLine(M, b_1) → c_1
  29. OrthogonalLine(K, a_1) → d_1
  30. Intersect(c_1, d_1) → N
  31. Segment(L, M) → e_1
  32. Segment(K, N) → g_1
  33. Segment(N, M) → f_1
  34. Segment(K, M) → h_1
  35. Segment(L, N) → i_1
  36. Intersect(h_1, i_1) → O
  37. Circle(P, Q) → k_1
  38. Segment(P, Q) → j_1
  39. OrthogonalLine(P, j_1) → l_1
  40. OrthogonalLine(Q, j_1) → m_1
  41. Intersect(k_1, l_1, 2) → S
  42. Line(S, j_1) → n_1
  43. Intersect(m_1, n_1) → R
  44. Segment(P, S) → p_1
  45. Segment(S, R) → q_1
  46. Segment(P, R) → s_1
  47. Segment(Q, S) → t_1
  48. Intersect(s_1, t_1) → T
  49. Segment(Q, R) → r_1
  50. Segment(W, U) → a_2
  51. Segment(U, V) → b_2
  52. Segment(V, W) → c_2
  53. Mirror(V, a_2) → X
  54. Segment(W, X) → d_2
  55. Segment(X, U) → e_2
  56. Segment(V, X) → f_2
  57. Intersect(a_2, f_2) → Z
  58. Segment(A_1, B_1) → g_2
  59. Segment(A_1, C_1) → h_2
  60. Line(C_1, g_2) → i_2
  61. Point(i_2) → D_1
  62. Segment(B_1, D_1) → j_2
  63. Segment(C_1, D_1) → k_2
  64. Segment(C_1, B_1) → l_2
  65. Segment(A_1, D_1) → m_2
  66. Intersect(l_2, m_2) → E_1
  67. Segment(C, E) → n_2
  68. Segment(E, B) → p_2
  69. Segment(D, E) → q_2
  70. Segment(E, A) → r_2
  71. Angle(A, B, E) → α
  72. Angle(E, B, D) → β
  73. Angle(B, D, E) → γ
  74. Angle(E, D, C) → δ
  75. Angle(D, C, E) → β_1
  76. Angle(E, C, A) → γ_1
  77. Angle(C, A, E) → δ_1
  78. Angle(E, A, B) → ε_1
  79. Angle(D, E, B) → ζ_1
  80. Segment(G, J) → s_2
  81. Segment(J, I) → t_2
  82. Segment(F, J) → a_3
  83. Segment(J, H) → b_3
  84. Angle(J, H, I) → ε
  85. Angle(H, I, J) → ζ
  86. Angle(J, I, F) → η
  87. Angle(I, F, J) → θ
  88. Angle(J, F, G) → η_1
  89. Angle(F, G, J) → θ_1
  90. Angle(J, G, H) → ι_1
  91. Angle(G, H, J) → κ_1
  92. Angle(I, J, H) → λ_1
  93. Segment(K, O) → c_3
  94. Segment(O, M) → d_3
  95. Segment(L, O) → e_3
  96. Segment(O, N) → f_3
  97. Angle(L, M, O) → ι
  98. Angle(O, M, N) → κ
  99. Angle(M, N, O) → λ
  100. Angle(O, N, K) → μ
  101. Angle(N, K, O) → μ_1
  102. Angle(O, K, L) → ν_1
  103. Angle(K, L, O) → ξ_1
  104. Angle(O, L, M) → ο_1
  105. Angle(K, O, N) → ρ_1
  106. Segment(S, T) → g_3
  107. Segment(T, Q) → h_3
  108. Segment(P, T) → i_3
  109. Segment(T, R) → j_3
  110. Angle(T, S, R) → ν
  111. Angle(S, R, T) → ξ
  112. Angle(T, R, Q) → ο
  113. Angle(R, Q, T) → ρ
  114. Angle(T, Q, P) → σ_1
  115. Angle(Q, P, T) → τ_1
  116. Angle(T, P, S) → υ_1
  117. Angle(P, S, T) → φ_1
  118. Angle(Q, T, R) → χ_1
  119. Angle(X, Z, W) → σ
  120. Angle(U, W, X) → τ
  121. Angle(W, X, V) → υ
  122. Angle(V, X, U) → φ
  123. Angle(X, U, W) → ψ_1
  124. Angle(W, U, V) → ω_1
  125. Angle(U, V, X) → α_2
  126. Angle(X, V, W) → β_2
  127. Angle(V, W, U) → γ_2
  128. Segment(W, U) → k_3
  129. Segment(V, X) → l_3
  130. Midpoint(V, Z) → F_1
  131. Midpoint(Z, X) → G_1
  132. Distance(V, Z) → distanceVZ
  133. Distance(V, Z) → o
  134. Distance(W, Z) → u
  135. Distance(U, Z) → v
  136. Midpoint(Z, W) → H_1
  137. Midpoint(U, Z) → I_1
  138. Segment(C_1, E_1) → m_3
  139. Segment(E_1, B_1) → n_3
  140. Segment(E_1, D_1) → p_3
  141. Segment(E_1, A_1) → q_3
  142. Angle(E_1, A_1, B_1) → χ
  143. Angle(A_1, B_1, E_1) → ψ
  144. Angle(E_1, B_1, D_1) → ω
  145. Angle(B_1, D_1, E_1) → α_1
  146. Angle(E_1, D_1, C_1) → δ_2
  147. Angle(D_1, C_1, E_1) → ε_2
  148. Angle(E_1, C_1, A_1) → ζ_2
  149. Angle(C_1, A_1, E_1) → η_2

AI Drawing Prompt Reference

Draw a quadrilateral ABCD and connect its diagonals AC and BD, marking their intersection as E. Then draw circles with E as the center and A, B, C, D on the circumference, marking the intersection points as F. Next, draw quadrilateral AEDF and connect its diagonals AF and DE, marking their intersection as G. Finally, draw quadrilateral AEGF and connect its diagonals AG and EF, marking their intersection as H.
The prompt above was compiled from the original drawing commands and is for reference only.