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Isosceles Trapezoid Investigation by Julie Arakelian

Isosceles Trapezoid Investigation by Julie Arakelian
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2018-03-09 20:49
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This example demonstrates the geometric properties and transformations of an isosceles trapezoid. It involves core concepts like angles, trapezoids, dilation, frequency distribution, variance, normal distribution, and integral calculus. The construction uses commands such as Line, Ray, Point, Midpoint, Slope, OrthogonalLine, Mirror, Dilate, Segment, Circle, Intersect, Vector, Translate, Angle, Rotate, Polygon, and Distance. It is suitable for high school mathematics teaching, exploring geometric transformations and data analysis.

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') → C
  34. Segment(D, C) → 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_1
  46. Dilate(A, If[5 < o ≤ 6, 6 - o, 0], B) → A'_4
  47. Vector(A, A'_4) → v
  48. Dilate(D, If[7 < o ≤ 8, 8 - o, 0], I') → I'_2
  49. Vector(D, I'_2) → w
  50. Dilate(A, If[9 < o ≤ 10, 10 - o, 0], I') → A'_5
  51. Segment(A, A'_5) → i_1
  52. Dilate(A, If[10 < o ≤ 11, 11 - o, 0], D) → A'_6
  53. Vector(A, A'_6) → u_1
  54. Translate(A, u_1) → A'_7
  55. Translate(A'_5, u_1) → Q
  56. Segment(A'_7, Q) → j_1
  57. Segment(D, B) → l_1
  58. Angle(L, A, I') → γ
  59. Rotate(A'_7, If[11 < o ≤ 12, ((-(o - 11)) * (2 * γ)), (-2 * γ)], D) → R
  60. Rotate(Q, If[11 < o ≤ 12, ((-(o - 11)) * (2 * γ)), (-2 * γ)], D) → Q'
  61. Segment(R, Q') → m_1
  62. Polygon(A, B, I', D) → poly1, a_2, c_2, i', i_2
  63. Intersect(i_1, m_1) → E
  64. Distance(A, E) → distanceAS
  65. Distance(E, C_1) → distanceSN'
  66. Distance(E, B) → distanceSC
  67. Distance(E, D) → distanceSI
  68. Segment(B, I') → q''