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Tangram Puzzles

Tangram Puzzles
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2020-07-11 12:31
PolygonAngleTransformationGeometric Construction
This example demonstrates how to use tangram pieces to form various shapes. It involves core mathematical concepts such as geometric construction, symmetry, rotation, and translation. Key GeoGebra commands and objects used include Point, Segment, Polygon, Rotate, and Circle, as detailed in the construction summary. Suitable for middle school students to learn geometric constructions and spatial reasoning.

GeoGebra Commands & Parameters

  1. Point(Circle[C, a]) → D
  2. Segment(C, D) → b
  3. Semicircle(C, D) → c
  4. Midpoint(b) → E
  5. OrthogonalLine(E, b) → d
  6. Intersect(c, d, 1) → F
  7. Polygon(D, F, C) → poly1, c_1, d_1, f
  8. Point(Circle[G, a]) → H
  9. Segment(G, H) → e
  10. Semicircle(G, H) → g
  11. Midpoint(e) → I
  12. OrthogonalLine(I, e) → h
  13. Intersect(g, h, 1) → J
  14. Polygon(G, H, J) → poly2, j, g_1, h_1
  15. Point(Circle[A, a / 2]) → B
  16. Segment(A, B) → i
  17. OrthogonalLine(A, i) → k
  18. Circle(A, B) → p
  19. Intersect(p, k, 2) → K
  20. Polygon(A, B, K) → poly3, k_1, a_1, b_1
  21. Point(Circle[L, a / 2]) → M
  22. Segment(L, M) → l
  23. Semicircle(L, M) → q
  24. Midpoint(l) → N
  25. OrthogonalLine(N, l) → m
  26. Intersect(q, m, 1) → O
  27. Polygon(L, M, O) → poly4, o, l_1, m_1
  28. Point(Circle[P, a / 2]) → Q
  29. Segment(P, Q) → n
  30. Semicircle(P, Q) → r
  31. Midpoint(n) → R
  32. OrthogonalLine(R, n) → s
  33. Intersect(r, s, 1) → S
  34. Polygon(P, Q, S) → poly5, s_1, p_1, q_1
  35. Point(Circle[T, (a * sqrt(2) / 4)]) → U
  36. Segment(T, U) → t
  37. OrthogonalLine(T, t) → e_1
  38. OrthogonalLine(U, t) → f_1
  39. Circle(T, U) → r_1
  40. Circle(U, T) → t_1
  41. Intersect(t_1, f_1, 2) → V
  42. Intersect(r_1, e_1, 2) → W
  43. Polygon(T, U, V, W) → poly6, t_2, u, v, w
  44. Point(Circle[Z, a / 2]) → A_1
  45. Segment(Z, A_1) → i_1
  46. Rotate(Z, 315°, A_1) → Z'
  47. Angle(Z', A_1, Z) → α
  48. Ray(A_1, Z') → j_1
  49. Circle(A_1, (a * sqrt(2) / 4)) → c_2
  50. Intersect(c_2, j_1, 1) → B_1
  51. Line(Z, j_1) → n_1
  52. Line(B_1, i_1) → a_2
  53. Intersect(n_1, a_2) → C_1
  54. Polygon(A_1, B_1, C_1, Z) → poly7, a_3, b_2, c_3, z
  55. Point(Circle[D_1, a]) → E_1