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Quadrilateral Playground

Quadrilateral Playground
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2015-12-24 12:32
PolygonTransformationGeometric Construction
Manipulate quadrilaterals to see which features change and which remain the same. This example covers quadrilaterals, parallelograms, rectangles, rhombuses, squares, and trapezoids. It uses commands like Segment, Line, Intersect, Angle, OrthogonalLine, Point, Circle, Mirror, etc., for construction. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(A, C) → b
  3. Line(B, b) → c
  4. Line(C, a) → d
  5. Intersect(c, d) → D
  6. Segment(B, D) → e
  7. Segment(C, D) → f
  8. Angle(B, A, C) → α
  9. Angle(C, D, B) → β
  10. Angle(D, B, A) → γ
  11. Angle(A, C, D) → δ
  12. Segment(E, F) → g
  13. Segment(E, G) → h
  14. Line(F, h) → i
  15. Line(G, g) → j
  16. Intersect(i, j) → H
  17. Segment(F, H) → k
  18. Segment(G, H) → l
  19. Segment(E, H) → m
  20. Segment(F, G) → n
  21. Intersect(m, n) → I
  22. Segment(E, I) → p
  23. Segment(I, H) → q
  24. Segment(F, I) → r
  25. Segment(I, G) → s
  26. Angle(I, E, G) → ε
  27. Angle(F, E, I) → ζ
  28. Angle(I, F, E) → η
  29. Angle(H, F, I) → θ
  30. Segment(J, K) → t
  31. OrthogonalLine(J, t) → a_1
  32. Point(a_1) → L
  33. Segment(J, L) → b_1
  34. OrthogonalLine(L, b_1) → c_1
  35. OrthogonalLine(K, t) → d_1
  36. Intersect(c_1, d_1) → M
  37. Segment(K, M) → e_1
  38. Segment(L, M) → f_1
  39. Angle(K, J, L) → ι
  40. Angle(J, L, M) → κ
  41. Angle(L, M, K) → λ
  42. Angle(M, K, J) → μ
  43. Segment(J, M) → g_1
  44. Segment(L, K) → h_1
  45. Intersect(g_1, h_1) → N
  46. Segment(J, N) → i_1
  47. Segment(N, M) → j_1
  48. Segment(L, N) → k_1
  49. Segment(N, K) → l_1
  50. Angle(N, J, L) → ν
  51. Angle(K, J, N) → ξ
  52. Angle(N, K, J) → ο
  53. Angle(M, K, N) → ρ
  54. Angle(G, I, E) → σ
  55. Angle(L, N, J) → τ
  56. Circle(O, P) → p_1
  57. Segment(P, O) → m_1
  58. Point(p_1) → Q
  59. Segment(O, Q) → n_1
  60. Line(Q, m_1) → q_1
  61. Line(P, n_1) → r_1
  62. Intersect(q_1, r_1) → R
  63. Segment(P, R) → s_1
  64. Segment(R, Q) → t_1
  65. Segment(O, R) → a_2
  66. Segment(Q, P) → b_2
  67. Intersect(a_2, b_2) → S
  68. Segment(O, S) → c_2
  69. Segment(S, R) → d_2
  70. Segment(Q, S) → e_2
  71. Segment(S, P) → f_2
  72. Angle(S, O, Q) → υ
  73. Angle(P, O, S) → ϕ
  74. Angle(S, P, O) → χ
  75. Angle(R, P, S) → ψ
  76. Angle(R, S, Q) → ω
  77. Circle(T, U) → g_2
  78. Segment(U, T) → h_2
  79. OrthogonalLine(T, h_2) → i_2
  80. Intersect(g_2, i_2, 1) → V
  81. Segment(T, V) → j_2
  82. Line(U, j_2) → k_2
  83. Line(V, h_2) → l_2
  84. Intersect(k_2, l_2) → W
  85. Segment(V, W) → m_2
  86. Segment(W, U) → n_2
  87. Angle(U, T, V) → α_1
  88. Angle(T, V, W) → β_1
  89. Angle(V, W, U) → γ_1
  90. Angle(W, U, T) → δ_1
  91. Segment(T, W) → p_2
  92. Segment(V, U) → q_2
  93. Intersect(p_2, q_2) → Z
  94. Segment(T, Z) → r_2
  95. Segment(Z, W) → s_2
  96. Segment(V, Z) → t_2
  97. Segment(Z, U) → a_3
  98. Angle(Z, T, V) → ε_1
  99. Angle(U, T, Z) → ζ_1
  100. Angle(Z, U, T) → η_1
  101. Angle(W, U, Z) → θ_1
  102. Angle(V, Z, T) → ι_1
  103. Circle(A_1, B_1) → c_3
  104. Segment(B_1, A_1) → b_3
  105. Point(c_3) → C_1
  106. Segment(A_1, C_1) → d_3
  107. Segment(B_1, C_1) → e_3
  108. OrthogonalLine(A_1, e_3) → f_3
  109. Point(f_3) → D_1
  110. Circle(D_1, B_1) → g_3
  111. Segment(B_1, D_1) → h_3
  112. Segment(D_1, C_1) → i_3
  113. Segment(A_1, D_1) → j_3
  114. Intersect(e_3, j_3) → E_1
  115. Segment(B_1, E_1) → k_3
  116. Segment(E_1, C_1) → l_3
  117. Segment(A_1, E_1) → m_3
  118. Segment(E_1, D_1) → n_3
  119. Angle(E_1, A_1, C_1) → κ_1
  120. Angle(B_1, A_1, E_1) → λ_1
  121. Angle(E_1, B_1, A_1) → μ_1
  122. Angle(D_1, B_1, E_1) → ν_1
  123. Angle(A_1, C_1, E_1) → ξ_1
  124. Angle(E_1, C_1, D_1) → ο_1
  125. Angle(C_1, D_1, E_1) → ρ_1
  126. Angle(E_1, D_1, B_1) → σ_1
  127. Angle(C_1, E_1, A_1) → τ_1
  128. Segment(F_1, G_1) → p_3
  129. Line(H_1, p_3) → q_3
  130. Point(q_3) → I_1
  131. Segment(H_1, I_1) → r_3
  132. Segment(F_1, H_1) → s_3
  133. Segment(G_1, I_1) → t_3
  134. Segment(F_1, I_1) → a_4
  135. Segment(G_1, H_1) → b_4
  136. Intersect(a_4, b_4) → J_1
  137. Segment(F_1, J_1) → c_4
  138. Segment(J_1, I_1) → d_4
  139. Segment(G_1, J_1) → e_4
  140. Segment(J_1, H_1) → f_4
  141. Angle(J_1, F_1, G_1) → υ_1
  142. Angle(H_1, F_1, J_1) → ϕ_1
  143. Angle(J_1, H_1, F_1) → χ_1
  144. Angle(I_1, H_1, G_1) → ψ_1
  145. Angle(G_1, J_1, F_1) → ω_1
  146. Segment(K_1, L_1) → g_4
  147. Segment(L_1, M_1) → h_4
  148. OrthogonalLine(M_1, h_4) → i_4
  149. Mirror(L_1, i_4) → N_1
  150. Mirror(K_1, i_4) → O_1
  151. Segment(L_1, N_1) → j_4
  152. Segment(K_1, O_1) → k_4
  153. Segment(O_1, N_1) → l_4
  154. Segment(K_1, N_1) → m_4
  155. Segment(O_1, L_1) → n_4
  156. Intersect(m_4, n_4) → P_1
  157. Segment(K_1, P_1) → p_4
  158. Segment(P_1, N_1) → q_4
  159. Segment(L_1, P_1) → r_4
  160. Segment(P_1, O_1) → s_4
  161. Angle(P_1, K_1, O_1) → α_2
  162. Angle(L_1, K_1, P_1) → β_2
  163. Angle(P_1, L_1, K_1) → γ_2
  164. Angle(N_1, L_1, P_1) → δ_2
  165. Angle(K_1, O_1, P_1) → ε_2
  166. Angle(P_1, O_1, N_1) → ζ_2
  167. Angle(O_1, N_1, P_1) → η_2
  168. Angle(P_1, N_1, L_1) → θ_2
  169. Angle(O_1, P_1, K_1) → ι_2