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Quadrilateral Reflectional Symmetries

Quadrilateral Reflectional Symmetries
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2016-07-11 03:23
PolygonTransformationGeometric Construction
This example demonstrates the reflectional symmetries of a quadrilateral. Key mathematical concepts include reflection transformation and geometric construction. Using GeoGebra commands such as Segment, Line, Intersect, Vector, Translate, Midpoint, and Polygon, the reflection symmetries of a quadrilateral can be constructed. Suitable for middle school and above students to learn about reflection transformations and geometric construction.

GeoGebra Commands & Parameters

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