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Trapezium Folding Demonstration

Trapezium Folding Demonstration
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2018-02-26 17:47
PolygonTransformationGeometric Construction
In collections Folding paper, doing geometry figures
This example demonstrates the geometric transformation and properties of a trapezium after folding. It involves core math concepts like polygons, geometric transformations (rotation), midpoints, line segments, and circle arcs. Construction highlights include commands such as Polygon, Midpoint, CircleArc, Segment, Rotate, Intersect, OrthogonalLine, Line, and Point. Suitable for high school geometry teaching to understand trapezium properties and transformation relationships.

GeoGebra Commands & Parameters

  1. Polygon(A, C, D, B) → vierhoek1, a, c, d, b
  2. Midpoint(B, D) → BD
  3. Midpoint(A, C) → F
  4. Midpoint(B, E) → G
  5. CircleArc(B, DD, D) → e
  6. Segment(B, E) → f
  7. Polygon(B, A, C, E) → vierhoek2, b_1, a_1, c_1, e_1
  8. Polygon(B, E, D) → driehoek1, d_1, b_2, e_2
  9. Rotate(B, (((-(s - 1)) * 180))°, e_1) → B'
  10. Rotate(E, (((-(s - 1)) * 180))°, e_1) → E'
  11. Rotate(D, (((-(s - 1)) * 180))°, e_1) → D'
  12. Polygon(B', E', D') → driehoek1', d', b', e'
  13. Polygon(DD, E, B) → driehoek2, b_3, dd, e_3
  14. Segment(G, F) → g
  15. Polygon(G, F, C, E) → vierhoek3, g_1, f_1, c_2, e_4
  16. Polygon(B, A, F, G) → vierhoek4, b_4, a_2, f_2, g_2
  17. Rotate(G, (((-(s - 3)) * 180))°, f_2) → G'
  18. Rotate(F, (((-(s - 3)) * 180))°, f_2) → F'
  19. Rotate(C, (((-(s - 3)) * 180))°, f_2) → C'
  20. Rotate(E, (((-(s - 3)) * 180))°, f_2) → E'_1
  21. Polygon(G', F', C', E'_1) → vierhoek3', g', f', c', e'_1
  22. Polygon(A, F, G, DD) → vierhoek5, a_3, f_3, g_3, dd_1
  23. Polygon(FE, A, F) → driehoek3, f_4, fe, a_4
  24. Segment(A, FA) → i
  25. Rotate(FE, (((-(s - 5)) * 180))°, i) → FE'
  26. Rotate(A, (((-(s - 5)) * 180))°, i) → A'
  27. Rotate(F, (((-(s - 5)) * 180))°, i) → F'_1
  28. Polygon(B, A, FA, G) → vierhoek6, r, t, i_1, j_1
  29. Intersect(g_3, i) → H
  30. OrthogonalLine(H, g', xOyPlane) → j
  31. Line(BD, F) → n
  32. Point(n) → K
  33. CircleArc(K, C, A) → p
  34. Polygon(G, H, F) → driehoek4, f_6, g_5, h_1
  35. Intersect(f_6, Line[FE, GG]) → J
  36. OrthogonalLine(H, b) → k
  37. CircleArc(A, F, FB) → h
  38. Polygon(A, F, FA) → driehoek5, fa, a_5, f_5
  39. Rotate(A, (((-(s - 5)) * 180))°, t) → A'_1
  40. Rotate(F, (((-(s - 5)) * 180))°, t) → F'_2
  41. Rotate(FA, (((-(s - 5)) * 180))°, t) → FA'
  42. Polygon(A'_1, F'_2, FA') → driehoek5', fa', a'_1, f'_2
  43. Line(DD, GG) → l
  44. Intersect(l, i) → I
  45. Polygon(G, DD, I, FA) → vierhoek7, g_4, dd_2, i_2, fa_1
  46. Line(FB, FA) → m
  47. Intersect(m, g_4) → M
  48. Segment(M, G) → q
  49. Segment(DD, I) → k_1
  50. Segment(DD, M) → l_1

AI Drawing Prompt Reference

Draw a trapezoid and demonstrate its geometric transformation after folding. Start by constructing the trapezoid, then find the midpoints of the non-parallel sides and connect them to form a new quadrilateral. Next, simulate the folding process using rotation, observing the shape changes and geometric relationships of the trapezoid after folding, including rotation angles, midpoints, line segments, and circular arcs.
The prompt above was compiled from the original drawing commands and is for reference only.