5-Piece Puzzle

5-Piece Puzzle
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2012-07-07 02:28
Move the five pieces to create any of the figures shown. This example involves geometric construction using commands such as Circle, Point, Line, Vector, Translate, Polygon, and Rotate. Suitable for middle school and above students to practice geometric shape assembly and transformation.

GeoGebra Commands & Parameters

  1. Circle(M, m) → p
  2. Circle(M, n) → q
  3. Point(q) → N
  4. Line(M, N) → r
  5. OrthogonalLine(M, r) → s
  6. Intersect(p, s, 1) → O
  7. Intersect(p, r, 1) → P
  8. Line(O, r) → t
  9. Line(P, s) → f_1
  10. Intersect(t, f_1) → Q
  11. Vector(P, M) → u
  12. Translate(Q, Vector[8 * u]) → Q'_1
  13. Vector(Q, P) → v
  14. Translate(Q, Vector[4 * v]) → Q'_2
  15. Polygon(Q'_2, Q, Q'_1) → poly7, q'_1, q', q_1
  16. Circle(R, m) → h_1
  17. Circle(R, o) → p_1
  18. Point(p_1) → S
  19. Line(S, R) → m_1
  20. OrthogonalLine(R, m_1) → n_1
  21. Intersect(h_1, n_1, 1) → T
  22. Intersect(h_1, m_1, 2) → U
  23. Line(U, n_1) → r_1
  24. Line(T, m_1) → s_1
  25. Intersect(r_1, s_1) → V
  26. Vector(T, R) → w
  27. Translate(V, Vector[3.576 * w]) → V'_1
  28. Vector(U, R) → z
  29. Translate(V, Vector[3.576 * z]) → V'_2
  30. Translate(V'_2, Vector[1.7888 * w]) → V''_1
  31. Polygon(V''_1, V'_2, V, V'_1) → poly8, v'', v', v_1, v'_1
  32. Circle(W, m) → t_1
  33. Circle(W, n) → f_2
  34. Point(f_2) → Z
  35. Line(Z, W) → a_2
  36. OrthogonalLine(W, a_2) → b_2
  37. Intersect(t_1, b_2, 1) → A_1
  38. Intersect(t_1, a_2, 2) → B_1
  39. Line(A_1, a_2) → h_2
  40. Line(B_1, b_2) → i_2
  41. Intersect(i_2, h_2) → C_1
  42. Vector(A_1, W) → u_1
  43. Translate(C_1, Vector[3.576 * u_1]) → D_1
  44. Vector(B_1, W) → w_1
  45. Translate(C_1, Vector[3.576 * w_1]) → E_1
  46. Translate(D_1, Vector[3.576 * w_1]) → F_1
  47. Polygon(E_1, C_1, D_1, F_1) → poly9, e_3, c_3, d_3, f_3
  48. Circle(G_1, a_4) → k_2
  49. Circle(G_1, b_4) → p_2
  50. Point(p_2) → H_1
  51. Line(H_1, G_1) → j_2
  52. OrthogonalLine(G_1, j_2) → m_2
  53. Intersect(k_2, j_2, 2) → I_1
  54. Intersect(k_2, m_2, 1) → J_1
  55. Line(I_1, m_2) → n_2
  56. Line(J_1, j_2) → q_2
  57. Intersect(n_2, q_2) → K_1
  58. Point(n_2) → L_1
  59. Rotate(L_1, 63.43*°, I_1) → M_1
  60. Angle(L_1, I_1, M_1) → γ
  61. Segment(I_1, L_1) → r_2
  62. Vector(I_1, M_1) → z_1
  63. Rotate(I_1, 270*°, M_1) → N_1
  64. Angle(N_1, M_1, I_1) → δ
  65. Vector(M_1, N_1) → u_2
  66. Vector(J_1, G_1) → v_2
  67. Vector(I_1, G_1) → w_2
  68. Translate(K_1, Vector[2.5 * v_2]) → O_1
  69. Translate(K_1, Vector[5 * w_2]) → P_1
  70. Translate(O_1, Vector[1.118 * z_1]) → Q_1
  71. Translate(Q_1, Vector[2.235 * u_2]) → R_1
  72. Translate(R_1, Vector[2.235 * z_1]) → S_1
  73. Polygon(P_1, K_1, O_1, Q_1, R_1, S_1) → poly10, p_3, k_3, o_1, q_3, r_3, s_2
  74. Circle(T_1, a) → t_2
  75. Circle(T_1, b) → g_3
  76. Point(g_3) → U_1
  77. Line(U_1, T_1) → h_3
  78. OrthogonalLine(T_1, h_3) → i_3
  79. Intersect(t_2, i_3, 1) → V_1
  80. Intersect(t_2, h_3, 2) → W_1
  81. Line(V_1, h_3) → j_3
  82. Line(W_1, i_3) → m_3
  83. Intersect(j_3, m_3) → Z_1
  84. Vector(V_1, T_1) → z_2
  85. Vector(W_1, T_1) → u_3
  86. Translate(Z_1, Vector[2.9813 * z_2]) → A_2
  87. Translate(Z_1, Vector[5.96 * u_3]) → B_2
  88. Polygon(B_2, Z_1, A_2) → poly11, a_5, b_5, z_3
  89. Mirror(V''_1, m_1) → V'''
  90. Mirror(V'_2, m_1) → V''
  91. Mirror(V, m_1) → V'
  92. Mirror(V'_1, m_1) → D
  93. Polygon(V''', V'', V', D) → poly8', v''', v''_1, v'_2, d
  94. Intersect(h_1, n_1) → A, B
  95. CircleSector(U, B, A) → c
  96. Point(c) → C
  97. Angle(C, U, B) → α
  98. Intersect(t_2, i_3, 2) → E
  99. CircleSector(W_1, E, V_1) → e
  100. Point(e) → F
  101. Angle(E, W_1, F) → β
  102. Mirror(B_2, h_3) → G
  103. Mirror(Z_1, h_3) → H
  104. Mirror(A_2, h_3) → I
  105. Polygon(G, H, I) → poly11', i, g, h
  106. Intersect(k_2, m_2, 2) → J
  107. CircleSector(I_1, J, J_1) → f
  108. Point(f) → K
  109. Angle(J, I_1, K) → ε
  110. Mirror(P_1, j_2) → L
  111. Mirror(K_1, j_2) → C_2
  112. Mirror(O_1, j_2) → D_2
  113. Mirror(Q_1, j_2) → E_2
  114. Mirror(R_1, j_2) → F_2
  115. Mirror(S_1, j_2) → G_2
  116. Polygon(L, C_2, D_2, E_2, F_2, G_2) → poly10', l, c_2, d_2, e_2, f_4, g_2
  117. Intersect(p, s, 2) → H_2
  118. CircleSector(P, O, H_2) → k
  119. Point(k) → I_2
  120. Angle(O, P, I_2) → ζ
  121. Mirror(Q'_2, r) → Q''
  122. Mirror(Q, r) → Q'
  123. Mirror(Q'_1, r) → J_2
  124. Polygon(Q'', Q', J_2) → poly7', j_1, q'', q'_2

AI Drawing Prompt Reference

Draw a 5-piece puzzle made of geometric shapes. The shapes include a circle, a triangle, a square, and a rhombus. These shapes are connected through rotation and translation to form a complete puzzle. The puzzle should show the relative positions and transformation relationships between the shapes.
The prompt above was compiled from the original drawing commands and is for reference only.