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Tangram Puzzle Cat (Rotations and Translations)

Tangram Puzzle Cat (Rotations and Translations)
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2017-02-06 08:02
PolygonTransformationGeometric Construction
This example demonstrates how to recreate a cat picture using Tangram pieces, focusing on geometric transformations such as rotations and translations. Key math concepts include transformations, geometry, and spatial reasoning. GeoGebra commands like Point, Segment, Semicircle, Midpoint, OrthogonalLine, Intersect, Polygon, Circle, Rotate, Angle, Ray, and Line are used to construct the shapes. Suitable for middle school students learning geometric transformations and spatial visualization.

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