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Isosceles Trapezoid Reflection

Isosceles Trapezoid Reflection
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2016-07-11 03:15
VectorTransformationGeometric Construction
This example demonstrates the geometric properties of an isosceles trapezoid through reflection transformation. Core math concepts include reflection, isosceles trapezoid, parametric curves, correlation, stochastic process, constructions, and dilation. Key GeoGebra commands used are Segment, Line, LineBisector, Mirror, Vector, Translate, Midpoint, and Polygon. Suitable for high school mathematics education, illustrating the application of geometric transformations and parametric equations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(A, C) → g
  3. Line(C, f) → h
  4. LineBisector(A, B) → i
  5. Mirror(C, i) → C'
  6. Segment(C', B) → j
  7. Segment(C, C') → k
  8. Vector(D, E) → u
  9. Vector(F, G) → v
  10. Vector(H, I) → w
  11. Translate(A, u) → A'
  12. Translate(B, u) → B'
  13. Segment(A', B') → f'
  14. Translate(A, u) → A'_1
  15. Translate(C, u) → C'_1
  16. Segment(A'_1, C'_1) → g'
  17. Translate(C', u) → C''
  18. Translate(B, u) → B'_1
  19. Segment(C'', B'_1) → j'
  20. Translate(C, u) → C'_2
  21. Translate(C', u) → C''_1
  22. Segment(C'_2, C''_1) → k'
  23. Translate(A, v) → A'_2
  24. Translate(B, v) → B'_2
  25. Segment(A'_2, B'_2) → f'_1
  26. Translate(A, v) → A'_3
  27. Translate(C, v) → C'_3
  28. Segment(A'_3, C'_3) → g'_1
  29. Translate(C', v) → C''_2
  30. Translate(B, v) → B'_3
  31. Segment(C''_2, B'_3) → j'_1
  32. Translate(C, v) → C'_4
  33. Translate(C', v) → C''_3
  34. Segment(C'_4, C''_3) → k'_1
  35. Translate(A, w) → A'_4
  36. Translate(B, w) → B'_4
  37. Segment(A'_4, B'_4) → f'_2
  38. Translate(A, w) → A'_5
  39. Translate(C, w) → C'_5
  40. Segment(A'_5, C'_5) → g'_2
  41. Translate(C', w) → C''_4
  42. Translate(B, w) → B'_5
  43. Segment(C''_4, B'_5) → j'_2
  44. Translate(C, w) → C'_6
  45. Translate(C', w) → C''_5
  46. Segment(C'_6, C''_5) → k'_2
  47. Midpoint(C, C') → J
  48. Midpoint(A, B) → K
  49. Midpoint(C'_1, A') → L
  50. Midpoint(C'', B') → M
  51. Line(J, K) → l
  52. Line(L, M) → m
  53. Line(C'_5, B'_4) → n
  54. Line(A'_2, C''_2) → p
  55. Polygon(C, J, K, A) → poly1, c, j_1, k_1, a
  56. Polygon(C'_1, C'', M, L) → poly2, c'_1, c'', m_1, l_1
  57. Polygon(C'_5, B'_4, A'_4) → poly3, a'_4, c'_5, b'_4
  58. Polygon(A'_2, C'_3, C''_2) → poly4, c''_2, a'_2, c'_3