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Rectangle Rotational Symmetry Demo

Rectangle Rotational Symmetry Demo
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2019-02-26 07:55
PolygonTransformationGeometric Construction
This example demonstrates the rotational symmetry of a rectangle by rotating it and observing the angles and positions at which it coincides with its original shape, revealing its symmetric properties. Core mathematical concepts include rotational symmetry, angles, geometric transformations, and geometric construction. It utilizes commands/objects like Segment, OrthogonalLine, Point, Intersect, Polygon, Circle, Line, Rotate, and Mirror from GeoGebra. Suitable for middle school students and above learning geometric transformations, symmetry, and applying GeoGebra for exploratory geometry.

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. Polygon(C, D, B, A) → poly1, c_1, d_1, b_1, a_1
  8. Segment(C, B) → e
  9. Segment(D, A) → f
  10. Intersect(e, f) → E
  11. Segment(K, L) → l
  12. Circle(K, L) → p
  13. Point(p) → M
  14. Segment(K, M) → m
  15. Line(M, l) → n
  16. Line(L, m) → q
  17. Intersect(n, q) → N
  18. Segment(M, L) → r
  19. Segment(N, K) → s
  20. Intersect(r, s) → O
  21. Rotate(C, (-α), E) → C'
  22. Rotate(D, (-α), E) → D'
  23. Rotate(B, (-α), E) → B'
  24. Rotate(A, (-α), E) → A'
  25. Polygon(C', D', B', A') → poly1', c', d', b', a'
  26. Rotate(M, (-α), O) → M'
  27. Rotate(N, (-α), O) → N'
  28. Rotate(L, (-α), O) → L'
  29. Rotate(K, (-α), O) → K'
  30. Polygon(M', N', L', K') → poly3', m', n', l', k'
  31. Segment(P, Q) → t
  32. Segment(P, R) → e_1
  33. Line(Q, e_1) → g_1
  34. Line(R, t) → h_1
  35. Intersect(g_1, h_1) → S
  36. Segment(R, Q) → i_1
  37. Segment(S, P) → j_1
  38. Intersect(i_1, j_1) → T
  39. Rotate(P, (-α), T) → P'
  40. Rotate(R, (-α), T) → R'
  41. Rotate(S, (-α), T) → S'
  42. Rotate(Q, (-α), T) → Q'
  43. Segment(U, V) → t_1
  44. Line(W, t_1) → b_2
  45. Point(b_2) → Z
  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. Line(B_1, C_1) → f_2
  54. Mirror(D_1, f_2) → E_1
  55. Segment(D_1, E_1) → g_2
  56. Intersect(f_2, g_2) → F_1
  57. Rotate(D_1, (-α), F_1) → G_1
  58. Rotate(B_1, (-α), F_1) → H_1
  59. Rotate(E_1, (-α), F_1) → I_1
  60. Rotate(C_1, (-α), F_1) → J_1
  61. Polygon(G_1, H_1, I_1, J_1) → poly6', g_3, h_2, i_2, j_2
  62. Intersect(c', a') → H
  63. Intersect(c_1, a_1) → I