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Trapezoid Reflection

Trapezoid Reflection
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2016-07-11 02:57
PolygonAngleVectorTransformationGeometric Construction
This example demonstrates the reflection transformation of a trapezoid. Key mathematical concepts include reflection transformation, properties of trapezoids, and angle relationships. Using GeoGebra commands such as Segment, Line, Point, Vector, Translate, etc., the trapezoid and its reflected image are constructed. Suitable for middle school and above students to learn geometric transformations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Line(C, f) → g
  3. Segment(C, A) → i
  4. Point(g) → D
  5. Segment(B, D) → j
  6. Segment(D, C) → k
  7. Vector(E, F) → u
  8. Vector(G, H) → v
  9. Vector(I, J) → w
  10. Translate(A, u) → A'
  11. Translate(B, u) → B'
  12. Segment(A', B') → f'
  13. Translate(C, u) → C'
  14. Translate(A, u) → A'_1
  15. Segment(C', A'_1) → i'
  16. Translate(B, u) → B'_1
  17. Translate(D, u) → D'
  18. Segment(B'_1, D') → j'
  19. Translate(D, u) → D'_1
  20. Translate(C, u) → C'_1
  21. Segment(D'_1, C'_1) → k'
  22. Translate(A, v) → A'_2
  23. Translate(B, v) → B'_2
  24. Segment(A'_2, B'_2) → f'_1
  25. Translate(C, v) → C'_2
  26. Translate(A, v) → A'_3
  27. Segment(C'_2, A'_3) → i'_1
  28. Translate(B, v) → B'_3
  29. Translate(D, v) → D'_2
  30. Segment(B'_3, D'_2) → j'_1
  31. Translate(D, v) → D'_3
  32. Translate(C, v) → C'_3
  33. Segment(D'_3, C'_3) → k'_1
  34. Translate(A, w) → A'_4
  35. Translate(B, w) → B'_4
  36. Segment(A'_4, B'_4) → f'_2
  37. Translate(C, w) → C'_4
  38. Translate(A, w) → A'_5
  39. Segment(C'_4, A'_5) → i'_2
  40. Translate(B, w) → B'_5
  41. Translate(D, w) → D'_4
  42. Segment(B'_5, D'_4) → j'_2
  43. Translate(D, w) → D'_5
  44. Translate(C, w) → C'_5
  45. Segment(D'_5, C'_5) → k'_2
  46. Midpoint(C, A) → K
  47. Midpoint(D, B) → L
  48. Midpoint(C', D') → M
  49. Midpoint(A', B') → N
  50. Line(K, L) → h
  51. Line(M, N) → l
  52. Line(C'_4, B'_4) → m
  53. Line(A'_2, D'_2) → n
  54. Polygon(K, L, D, C) → poly1, k_1, l_1, d, c
  55. Polygon(C', M, N, A') → poly2, c', m_1, n_1, a'
  56. Polygon(A'_2, D'_2, C'_2) → poly3, c'_2, a'_2, d'_2
  57. Polygon(C'_4, B'_4, D'_4) → poly4, d'_4, c'_4, b'_4