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Exploring Tangram Geometry with GeoGebra

Exploring Tangram Geometry with GeoGebra
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2023-10-01 17:54
TrianglePolygonAngleTransformationGeometric Construction
In collections Tangram & Maths
This GeoGebra example demonstrates how a Tangram set (seven polygonal pieces) can be constructed and then transformed to form different target figures. It highlights the key phenomenon that the same collection of basic shapes can be rearranged—by geometric transformations—while preserving congruence properties and area relationships. The mathematical ideas include polygonal decomposition, constructing shapes from intersections, and using rotations to position pieces precisely for拼合 (tiling/pattern formation). In the construction, the example relies on Polygon to create the tangram pieces (e.g., poli1, poli2, poli3, poli4); Segment and Line to define edges and auxiliary straight lines; Midpoint and Intersect to compute critical vertices that determine the boundaries of the pieces (using objects like a_1, b_1, c_1, g_1 and reference frames frame1–frame5); and Rotate to carry out the transformation of pieces into the required configurations (objects such as j/J, N/O/P, and K/L/M help specify the placement targets). Suitable for middle and high school geometry, classroom activities on geometric construction and transformation, and student exploration of how complex patterns emerge from simple polygons.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poli1, frame3, frame4, frame1, frame2, C, D
  2. Segment(A, C) → frame12
  3. Midpoint(D, C) → E
  4. Midpoint(D, A) → F
  5. Segment(F, E) → frame5
  6. Midpoint(A, C) → G
  7. Segment(B, G) → frame9
  8. Midpoint(F, E) → H
  9. Midpoint(G, C) → I
  10. Segment(H, I) → frame7
  11. Segment(G, H) → frame8
  12. Line(F, frame8) → j
  13. Intersect(j, frame12) → J
  14. Segment(F, J) → frame11
  15. Polygon(A, G, B) → poli2, b_1, a_1, g_1
  16. Point(Circle[N, b_1]) → O
  17. Rotate(O + (a_1, 0), Angle[B - G] + Angle[O - N] - Angle[G - A], O) → P
  18. Polygon(N, O, P) → poli4, p, n, o
  19. Polygon(B, G, C) → poli3, c_1, b_2, g_2
  20. Point(Circle[K, c_1]) → L
  21. Rotate(L + (b_2, 0), Angle[C - G] + Angle[L - K] - Angle[G - B], L) → M
  22. Polygon(K, L, M) → poli5, m, k_1, l
  23. Polygon(H, E, C, I) → poli6, h_1, e_1, c_2, i_1
  24. Point(Circle[Q, h_1]) → R
  25. Rotate(R + (e_1, 0), Angle[C - E] + Angle[R - Q] - Angle[E - H], R) → S
  26. Rotate(S + (c_2, 0), Angle[I - C] + Angle[S - R] - Angle[C - E], S) → T
  27. Polygon(Q, R, S, T) → poli7, q, r, s, t
  28. Polygon(H, G, I) → poli8, i_2, h_2, g_3
  29. Point(Circle[U, i_2]) → V
  30. Rotate(V + (h_2, 0), Angle[I - G] + Angle[V - U] - Angle[G - H], V) → W
  31. Polygon(U, V, W) → poli9, w, u, v
  32. Polygon(F, H, G, J) → poli10, f_1, h_3, g_4, j_1
  33. Point(Circle[Z, f_1]) → A_1
  34. Rotate(A_1 + (h_3, 0), Angle[G - H] + Angle[A_1 - Z] - Angle[H - F], A_1) → B_1
  35. Rotate(B_1 + (g_4, 0), Angle[J - G] + Angle[B_1 - A_1] - Angle[G - H], B_1) → C_1
  36. Polygon(Z, A_1, B_1, C_1) → poli11, z, a_2, b_3, c_3
  37. Polygon(F, J, A) → poli12, a_3, f_2, j_2
  38. Point(Circle[D_1, a_3]) → E_1
  39. Rotate(E_1 + (f_2, 0), Angle[A - J] + Angle[E_1 - D_1] - Angle[J - F], E_1) → F_1
  40. Polygon(D_1, E_1, F_1) → poli13, f_3, d_1, e_2
  41. Polygon(F, D, E) → poli14, e_3, f_4, d_2
  42. Point(Circle[G_1, e_3]) → H_1
  43. Rotate(H_1 + (f_4, 0), Angle[E - D] + Angle[H_1 - G_1] - Angle[D - F], H_1) → I_1
  44. Polygon(G_1, H_1, I_1) → poli15, i_3, g_5, h_4

AI Drawing Prompt Reference

Draw a tangram puzzle composed of seven polygonal pieces. Use geometric transformations such as rotation to assemble the basic shapes—a large rhombus, four corner triangles, two rectangles, and two squares—into a complete figure. The construction order involves creating the base pieces and then rotating them to fit into the target configuration, highlighting the principles of shape rearrangement and area preservation.
The prompt above was compiled from the original drawing commands and is for reference only.