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Tangram Puzzle - Rectangle

Tangram Puzzle - Rectangle
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2016-07-13 06:42
PolygonTransformationGeometric Construction
This example demonstrates how to rearrange the seven pieces of a tangram from a square into a rectangle. Key mathematical concepts include geometric transformations and area calculation. Using GeoGebra commands such as Point, Polygon, Segment, etc., the process of tangram assembly is dynamically illustrated. Suitable for high-grade elementary and junior high school students to learn geometric transformations and area calculation.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 6]) → B
  2. Polygon(A, B, C) → poly1, c, a_1, b
  3. Point(Circle[A_1, 6]) → B_1
  4. Polygon(A_1, B_1, C_1) → poly1_1, c_1, a_2, b_1
  5. Point(Circle[D, 3]) → E
  6. Polygon(D, E, F) → poly2, f, d, e
  7. Point(Circle[G, a / 2]) → H
  8. Segment(G, H) → g
  9. Semicircle(G, H) → h
  10. LineBisector(g) → i
  11. Intersect(h, i) → I,
  12. Polygon(G, H, I) → poly3, i_1, g_1, h_1
  13. Point(Circle[G_1, a / 2]) → H_1
  14. Segment(G_1, H_1) → g_3
  15. Semicircle(G_1, H_1) → h_3
  16. LineBisector(g_3) → i_3
  17. Intersect(h_3, i_3) → I_1,
  18. Polygon(G_1, H_1, I_1) → poly3_1, i_2, g_2, h_2
  19. Point(Circle[J, a / 2]) → K
  20. Segment(J, K) → j
  21. Midpoint(j) → L
  22. Circle(L, J) → k
  23. OrthogonalLine(L, j) → l
  24. Intersect(k, l) → M, N
  25. Polygon(J, M, K, N) → poly4, j_1, m, k_1, n
  26. Point(Circle[O, a / 2]) → P
  27. Segment(O, P) → p
  28. Rotate(O, -45*°, P) → O'
  29. Angle(O', P, O) → α
  30. Rotate(P, 135*°, O) → P'
  31. Angle(P, O, P') → β
  32. Ray(P, O') → q
  33. Ray(O, P') → r
  34. Circle(O, (a * sqrt(2) / 4)) → s
  35. Intersect(s, r) → Q,
  36. Intersect(s, q) → R, S
  37. Polygon(O, P, R, Q) → poly5, o, p_1, r_1, q_1

AI Drawing Prompt Reference

Draw a tangram puzzle showing the rearrangement from a square to a rectangle. Start with a large right triangle, then a smaller similar triangle, followed by a medium triangle. Next, construct a triangle using a semicircle and a perpendicular bisector, then another similar triangle. After that, form a square using a circle and a perpendicular line through its midpoint. Finally, create a quadrilateral using rays and a circle intersection. Arrange all pieces to maintain equal area, demonstrating geometric transformations and area calculation.
The prompt above was compiled from the original drawing commands and is for reference only.