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Tangram: Construct a Parallelogram

Tangram: Construct a Parallelogram
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2017-01-22 22:23
PolygonVectorGeometric Construction
This example demonstrates how to construct a parallelogram by dragging colored pieces onto a gray shape. Key mathematical concepts include geometric transformations and polygons. GeoGebra commands used include point, distance, polygon, segment, line, and perpendicular line. Suitable for middle and high school students learning geometric construction.

GeoGebra Commands & Parameters

  1. Point(Circle[S, 5]) → T
  2. Point(Circle[L, 3.54]) → O
  3. Distance(L, O) → o
  4. Point(Circle[C_2, o]) → D_2
  5. Point(Circle[D_2, o]) → G_2
  6. Polygon(C_2, D_2, 4) → poly12, g_3, h_3, i_3, j_3, E_2, F_2
  7. Point(Circle[F_2, o]) → H_2
  8. Point(Circle[H, 5]) → L_1
  9. Polygon(H, L_1, 4) → poly8, k_2, l_2, m_2, n_2, M_1, N_1
  10. Point(Circle[D, 10]) → B
  11. Segment(D, B) → j
  12. LineBisector(j) → j_2
  13. Intersect(j_2, j) → R
  14. Point(Circle[K, 5]) → G_1
  15. Segment(K, G_1) → g_2
  16. LineBisector(g_2) → k
  17. Intersect(j, k) → C
  18. Circle(R, 5) → e_2
  19. Intersect(e_2, j_2) → J, A_1
  20. Point(Circle[A, 10]) → H_1
  21. Segment(A, H_1) → h_2
  22. LineBisector(h_2) → i_2
  23. Intersect(i_2, h_2) → I_1
  24. Circle(I_1, 5) → d_2
  25. Intersect(d_2, i_2) → J_1, K_1
  26. Polygon(A, H_1, K_1) → poly1, a, b, c
  27. Polygon(B, D, J) → poly2, f, d, e
  28. Polygon(H, L_1, M_1) → poly3, g, h, i
  29. Line(D, E) → m
  30. Circle(K, 3.54) → q
  31. Intersect(q, k, 2) → N
  32. Polygon(N, K, G_1) → poly4, j_1, k_1, n_1
  33. Segment(L, O) → l
  34. Polygon(L, O, 4) → poly5, p, r, s, t, P, Q
  35. Segment(S, T) → g_1
  36. LineBisector(g_1) → h_1
  37. Circle(S, 3.54) → c_1
  38. Intersect(c_1, h_1) → U, V
  39. Polygon(S, T, V) → poly6, v, s_1, t_1
  40. Point(Circle[W, 5]) → Z
  41. Segment(W, Z) → i_1
  42. Line(F, H) → p_1
  43. OrthogonalLine(Z, i_1) → r_1
  44. Circle(Z, 2.5) → d_1
  45. Intersect(d_1, r_1) → D_1, E_1
  46. Line(E_1, i_1) → a_1
  47. Circle(Z, 3.54) → e_1
  48. Intersect(e_1, a_1, 2) → C_1
  49. Line(Z, C_1) → b_1
  50. Line(W, b_1) → f_2
  51. Intersect(f_2, a_1) → F_1
  52. Polygon(W, Z, C_1, F_1) → poly7, w_1, z_1, c_2, f_3
  53. Polygon(B_2, Z_1, B_1, A_2) → poly9, m_1, s_2, t_2, a_2
  54. Segment(H, L_1) → q_1
  55. Polygon(M, O_1, W_1) → poly10, n, f_1, l_1
  56. Polygon(O_1, M, P_1) → poly11, p_2, q_2, r_2
  57. Segment(C_2, D_2) → b_2
  58. Segment(D_2, G_2) → k_3
  59. Segment(F_2, H_2) → l_3
  60. Polygon(D_2, G_2, E_2) → poly13, e_3, d_3, g_4
  61. Polygon(H_2, C_2, F_2) → poly14, f_4, h_4, c_3