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Isosceles Trapezoid Construction by Julie Arakelian

Isosceles Trapezoid Construction by Julie Arakelian
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2018-03-09 09:00
PolygonCoordinate GeometryTransformationGeometric Construction
This example demonstrates the construction of an isosceles trapezoid. Key mathematical concepts include the properties of trapezoids, midpoints, slopes, orthogonal lines, mirroring, and rotation. Using GeoGebra commands such as Line, Point, Midpoint, Slope, OrthogonalLine, Mirror, Rotate, etc., an isosceles trapezoid is constructed. Suitable for students at the junior high school level and above to learn geometric construction and related concepts.

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''