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Rotational Symmetry of Quadrilaterals by youngcar

Rotational Symmetry of Quadrilaterals by youngcar
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2016-06-01 10:20
PolygonTransformationGeometric Construction
This example demonstrates the rotational symmetry in quadrilaterals, particularly trapezoids. Key math concepts include symmetry, rotation, and geometric construction. It utilizes GeoGebra commands like Segment, OrthogonalLine, Point, Intersect, Circle, Line, Rotate, Polygon, and Mirror to illustrate the concept. Suitable for middle school students and beyond for learning geometric transformations and symmetry, as well as for educational demonstrations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. OrthogonalLine(B, a) → c
  4. Point(b) → C
  5. OrthogonalLine(C, b) → d
  6. Intersect(c, d) → D
  7. Segment(C, B) → e
  8. Segment(D, A) → f
  9. Intersect(e, f) → E
  10. Segment(K, L) → l
  11. Circle(K, L) → p
  12. Point(p) → M
  13. Segment(K, M) → m
  14. Line(M, l) → n
  15. Line(L, m) → q
  16. Intersect(n, q) → N
  17. Segment(M, L) → r
  18. Segment(N, K) → s
  19. Intersect(r, s) → O
  20. Rotate(C, (-α), E) → C'
  21. Rotate(D, (-α), E) → D'
  22. Rotate(B, (-α), E) → B'
  23. Rotate(A, (-α), E) → A'
  24. Rotate(M, (-α), O) → M'
  25. Rotate(N, (-α), O) → N'
  26. Rotate(L, (-α), O) → L'
  27. Rotate(K, (-α), O) → K'
  28. Segment(P, Q) → t
  29. Segment(P, R) → e_1
  30. Line(Q, e_1) → g_1
  31. Line(R, t) → h_1
  32. Intersect(g_1, h_1) → S
  33. Segment(R, Q) → i_1
  34. Segment(S, P) → j_1
  35. Intersect(i_1, j_1) → T
  36. Rotate(P, (-α), T) → P'
  37. Rotate(R, (-α), T) → R'
  38. Rotate(S, (-α), T) → S'
  39. Rotate(Q, (-α), T) → Q'
  40. Segment(U, V) → t_1
  41. Segment(U, W) → a_2
  42. Line(W, t_1) → b_2
  43. Point(b_2) → Z
  44. Segment(Z, V) → c_2
  45. Polygon(U, V, Z, W) → poly5, u, v, z, w
  46. Segment(W, V) → d_2
  47. Segment(Z, U) → e_2
  48. Intersect(d_2, e_2) → A_1
  49. Rotate(U, (-α), A_1) → U'
  50. Rotate(V, (-α), A_1) → V'
  51. Rotate(Z, (-α), A_1) → Z'
  52. Rotate(W, (-α), A_1) → W'
  53. Polygon(U', V', Z', W') → poly5', u', v', z', w'
  54. Line(B_1, C_1) → f_2
  55. Mirror(D_1, f_2) → E_1
  56. Segment(D_1, E_1) → g_2
  57. Intersect(f_2, g_2) → F_1
  58. Rotate(D_1, (-α), F_1) → G_1
  59. Rotate(B_1, (-α), F_1) → H_1
  60. Rotate(E_1, (-α), F_1) → I_1
  61. Rotate(C_1, (-α), F_1) → J_1
  62. Intersect(z', w') → H
  63. Intersect(a_2, z) → I