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Trapezoid Midsegment Investigation

Trapezoid Midsegment Investigation
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2019-01-24 10:06
PolygonTrigonometryCoordinate GeometryGeometric ConstructionSlider Animation
This example dynamically illustrates the properties and theorems of the trapezoid's midsegment without words, lengths, or angle measures. Key guiding questions accompany the applet. It involves core concepts like trapezoid, midsegment, parallel lines, and geometric transformations, constructed using commands like Line, Ray, Point, Segment, Slope, Midpoint, Vector, Translate, Rotate in GeoGebra. Suitable for middle school and above mathematics education.

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