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Trapezium Dimensions

Trapezium Dimensions
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2018-02-26 17:50
PolygonGeometric Construction
In collections Folding paper, doing geometry figures
This example demonstrates the dimensions of a trapezium. Key mathematical concepts include the properties of trapeziums and geometric construction. Using GeoGebra commands such as Polygon, Midpoint, CircleArc, etc., the trapezium is constructed and the relationships between its sides and height are explored. Suitable for middle and high school students learning geometric construction and trapezium properties.

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
  51. Segment(B, D) → m_1
  52. Segment(D, C) → n_1
  53. Segment(G, E) → p_1
  54. Segment(A, C) → q_1
  55. Segment(G, BD) → r_1
  56. Segment(F, FA) → s_1