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Trapezoid Midsegment Dynamic Demo

Trapezoid Midsegment Dynamic Demo
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2017-11-30 12:49
Geometric Construction
This example dynamically illustrates the properties and theorems of the trapezoid midsegment, visually showing the relationship between the midsegment and the bases through interactive geometry. Key math concepts include trapezoid, midsegment theorem, and properties of parallel lines. Construction highlights GeoGebra commands like Line, Segment, Midpoint, Vector, and Translate used to build the trapezoid and midsegment. Suitable for middle school and above mathematics education for geometric intuition and theorem verification.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Ray(A, B) → g
  3. Point(g) → C
  4. Ray(A, C) → h
  5. Segment(A, C) → i
  6. Slope(f) → m
  7. PointIn(a) → D
  8. Segment(A, D) → j
  9. Line(D, i) → k
  10. Point(k) → E
  11. Ray(D, E) → l
  12. Point(l) → F
  13. Ray(D, F) → n
  14. Segment(F, C) → p
  15. Segment(D, F) → q
  16. Min(j, i) → c
  17. Circle(A, (0.2 * c)) → d
  18. Intersect(d, j, 1) → G
  19. Intersect(d, i, 1) → H
  20. CircleSector(A, H, G) → e
  21. Angle(C, A, D) → α
  22. CircleSector(A, G, H) → r
  23. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], C) → A'
  24. Midpoint(D, A) → I
  25. Midpoint(F, C) → J
  26. Segment(A, A') → s
  27. Dilate(F, If[0 < o ≤ 1, 1 - o, 0], D) → F'
  28. Segment(F, F') → t
  29. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], D) → A'_1
  30. Segment(A, A'_1) → f_1
  31. Ray(A, D) → g_1
  32. Point(g_1) → K
  33. Ray(D, K) → h_1
  34. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], D) → A'_2
  35. Vector(A, A'_2) → u
  36. Translate(e, u) → e'
  37. Dilate(A, If[3 < o ≤ 4, 4 - o, 0], I) → A'_3
  38. Dilate(C, If[3 < o ≤ 4, 4 - o, 0], J) → C'
  39. Segment(A, A'_3) → i_1
  40. Segment(C, C') → j_1
  41. Dilate(I, If[4 < o ≤ 5, 5 - o, 0], D) → I'
  42. Dilate(J, If[4 < o ≤ 5, 5 - o, 0], F) → J'
  43. Segment(I, I') → k_1
  44. Segment(J, J') → l_1
  45. Rotate(A, If[5 < o ≤ 6, ((o - 5) * π), π], I) → A'_4
  46. Rotate(A'_3, If[5 < o ≤ 6, ((o - 5) * π), π], I) → L
  47. Segment(A'_4, L) → m_1
  48. Polygon(A, C, F, D) → poly1, a_1, c_1, f_2, d_1
  49. Rotate(C, If[5 < o ≤ 6, ((-(o - 5)) * π), (-π)], J) → C'_1
  50. Rotate(C', If[5 < o ≤ 6, ((-(o - 5)) * π), (-π)], J) → C''
  51. Segment(C'_1, C'') → n_1
  52. Dilate(I, If[6 < o ≤ 7, 7 - o, 0], J) → I'_1
  53. Segment(I, I'_1) → p_1
  54. Dilate(D, If[7 < o ≤ 8, 8 - o, 0], I) → D'
  55. Vector(D, D') → v
  56. Translate(e', v) → e''
  57. Translate(r, u) → r'
  58. Translate(r', v) → r''
  59. Rotate(A, If[8.5 < o ≤ 9.5, ((-(o - 8.5)) * π), (-π)], J) → A'_5
  60. Rotate(C, If[8.5 < o ≤ 9.5, ((-(o - 8.5)) * π), (-π)], J) → C'_2
  61. Rotate(F, If[8.5 < o ≤ 9.5, ((-(o - 8.5)) * π), (-π)], J) → F'_1
  62. Rotate(D, If[8.5 < o ≤ 9.5, ((-(o - 8.5)) * π), (-π)], J) → D'_1
  63. Polygon(A'_5, C'_2, F'_1, D'_1) → poly1', a'_5, c'_2, f'_1, d'_1
  64. Dilate(I, If[10 < o ≤ 11, 11 - o, 0], D) → I'_2
  65. Vector(I, I'_2) → w
  66. Translate(I, w) → I'_3
  67. Translate(I'_1, w) → M
  68. Segment(I'_3, M) → q_1
  69. Dilate(I, If[11 < o ≤ 12, 12 - o, 0], M) → I'_4
  70. Dilate(I, If[11 < o ≤ 12, 12 - o, 0], M) → I'_5
  71. Vector(I, I'_5) → u_1
  72. Translate(I, u_1) → I'_6
  73. Translate(I'_1, u_1) → N
  74. Segment(I'_6, N) → r_1