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Parallelogram Reflection

Parallelogram Reflection
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2016-07-10 15:54
PolygonVectorCoordinate GeometryTransformationGeometric Construction
This example demonstrates the properties of a parallelogram under reflection transformation. It involves core math concepts like parallelogram, reflection, congruence, Pythagorean theorem, planes, and matrices. Construction highlights include using GeoGebra commands such as Segment, Line, Intersect, Vector, Translate, Midpoint, and Polygon. Suitable for high school mathematics teaching, illustrating the integration of geometric transformations and coordinate geometry.

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