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Isosceles Trapezoid (Scaffolded Discovery)

Isosceles Trapezoid (Scaffolded Discovery)
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2018-12-04 10:04
PolygonCoordinate GeometryTransformationGeometric Construction
This example demonstrates the geometric properties and transformations of an isosceles trapezoid. Core concepts include polygons, similarity transformations, linear equations, and geometric constructions. It utilizes commands like Line, Ray, Point, Midpoint, Slope, OrthogonalLine, Mirror, Dilate, Segment, Circle, Intersect, Vector, Translate, Angle, Rotate, Polygon, Distance. Suitable for high school mathematics education to explore symmetry and transformation patterns of isosceles trapezoids.

GeoGebra Commands & Parameters

  1. Line(A, B_1) → a
  2. Ray(A, B_1) → b
  3. Point(b) → B
  4. Midpoint(A, B) → D_1
  5. Line(A, B) → c
  6. Slope(c) → d
  7. OrthogonalLine(D_1, c) → g
  8. Point(g) → E_1
  9. Ray(D_1, E_1) → h
  10. Point(h) → F
  11. Slope(h) → i
  12. Line(F, c) → l
  13. Point(l) → G
  14. Point(l) → H
  15. Ray(F, G) → m
  16. Ray(F, H) → n
  17. Point(m) → D
  18. Mirror(D, h) → I'
  19. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'
  20. Segment(A, A') → p
  21. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], D) → A'_1
  22. Segment(A, A'_1) → q
  23. Segment(A, B) → r
  24. Segment(B, I') → s
  25. Segment(I', D) → t
  26. Segment(D, A) → a_1
  27. Circle(A, (0.2 * Min[a_1, r])) → c_1
  28. Circle(D, (0.2 * Min[a_1, r])) → d_1
  29. Intersect(d_1, a_1, 1) → J
  30. Intersect(d_1, t, 1) → K
  31. Intersect(c_1, r, 1) → L
  32. Intersect(c_1, a_1, 1) → M
  33. Dilate(D, If[2 < o ≤ 3, 3 - o, 0], I') → I'_1
  34. Segment(D, I'_1) → b_1
  35. Dilate(A, If[3 < o ≤ 4, 4 - o, 0], B) → A'_2
  36. Vector(A, A'_2) → u
  37. Translate(A, u) → A'_3
  38. Translate(A'_1, u) → N
  39. Segment(A'_3, N) → q'
  40. OrthogonalLine(A, r) → g_1
  41. Point(g_1) → O
  42. Angle(D, A, O) → α
  43. Angle(I', B, A) → β
  44. Rotate(A'_3, If[4 < o ≤ 5, (((o - 4) * 2) * α), (2 * α)], B) → P
  45. Rotate(N, If[4 < o ≤ 5, (((o - 4) * 2) * α), (2 * α)], B) → C
  46. Segment(P, C) → q''
  47. Dilate(A, If[5 < o ≤ 6, 6 - o, 0], B) → A'_4
  48. Vector(A, A'_4) → v
  49. Dilate(D, If[7 < o ≤ 8, 8 - o, 0], I') → I'_2
  50. Vector(D, I'_2) → w
  51. Dilate(A, If[9 < o ≤ 10, 10 - o, 0], I') → A'_5
  52. Segment(A, A'_5) → i_1
  53. Dilate(A, If[10 < o ≤ 11, 11 - o, 0], D) → A'_6
  54. Vector(A, A'_6) → u_1
  55. Translate(A, u_1) → A'_7
  56. Translate(A'_5, u_1) → Q
  57. Segment(A'_7, Q) → j_1
  58. Segment(D, B) → l_1
  59. Angle(L, A, I') → γ
  60. Rotate(A'_7, If[11 < o ≤ 12, ((-(o - 11)) * (2 * γ)), (-2 * γ)], D) → R
  61. Rotate(Q, If[11 < o ≤ 12, ((-(o - 11)) * (2 * γ)), (-2 * γ)], D) → Q'
  62. Segment(R, Q') → m_1
  63. Polygon(A, B, I', D) → poly1, a_2, c_2, i', i_2
  64. Intersect(i_1, m_1) → E
  65. Distance(A, E) → distanceAS
  66. Distance(E, C) → distanceSN'
  67. Distance(E, B) → distanceSC
  68. Distance(E, D) → distanceSI
  69. Angle(B, A, E) → δ
  70. Angle(E, B, A) → ε
  71. Angle(C, B, E) → ζ
  72. Angle(E, A, D) → η
  73. Angle(A, D, E) → θ
  74. Angle(E, D, C) → ι
  75. Angle(D, C, E) → κ
  76. Angle(B, E, C) → λ
  77. Angle(E, C, B) → μ
  78. Angle(A, E, B) → ν
  79. Polygon(A, B, C) → poly2, c_3, a_3, b_2
  80. Segment(A, C) → h_1
  81. Mirror(A, h_1) → A'_8
  82. Mirror(B, h_1) → B'
  83. Mirror(C, h_1) → C'
  84. Polygon(A'_8, B', C') → poly2', c', a'_8, b'
  85. Polygon(D, A, B) → poly3, b_3, d_2, a_4
  86. Segment(D, B) → p_1
  87. Mirror(D, p_1) → D'
  88. Mirror(A, p_1) → A'_9
  89. Mirror(B, p_1) → B'_1
  90. Polygon(D', A'_9, B'_1) → poly3', b'_1, d', a'_9