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Rotational Symmetry of Quadrilaterals: Square and Kite

Rotational Symmetry of Quadrilaterals: Square and Kite
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2017-12-12 14:42
CirclePolygonAngleTransformationGeometric Construction
In collections Rotational Symmetry 1
This GeoGebra example demonstrates the rotational and reflectional symmetry of quadrilaterals, focusing on squares and kites. It illustrates how geometric transformations such as rotation and mirroring reveal symmetry properties. The construction uses commands like Segment, OrthogonalLine, Point, Intersect, Polygon, Circle, Line, Rotate, Mirror, and PointIn to build a square and its rotated copies, along with kite shapes. Suitable for middle and high school geometry classes, it helps students visualize and compare the symmetry characteristics of different quadrilaterals, enhancing understanding of transformation 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. Segment(C, B) → e
  8. Segment(D, A) → f
  9. Intersect(e, f) → E
  10. Polygon(F, G, 4) → poly2, f_1, g, h, i, H, I
  11. Segment(I, G) → j
  12. Segment(H, F) → k
  13. Intersect(j, k) → J
  14. Segment(K, L) → l
  15. Circle(K, L) → p
  16. Point(p) → M
  17. Segment(K, M) → m
  18. Line(M, l) → n
  19. Line(L, m) → q
  20. Intersect(n, q) → N
  21. Segment(M, L) → r
  22. Segment(N, K) → s
  23. Intersect(r, s) → O
  24. Rotate(C, (-α), E) → C'
  25. Rotate(D, (-α), E) → D'
  26. Rotate(B, (-α), E) → B'
  27. Rotate(A, (-α), E) → A'
  28. Polygon(C', D', B', A') → poly1', c', d', b', a'
  29. Rotate(M, (-α), O) → M'
  30. Rotate(N, (-α), O) → N'
  31. Rotate(L, (-α), O) → L'
  32. Rotate(K, (-α), O) → K'
  33. Polygon(M', N', L', K') → poly3', m', n', l', k'
  34. Segment(P, Q) → t
  35. Segment(P, R) → e_1
  36. Line(Q, e_1) → g_1
  37. Line(R, t) → h_1
  38. Intersect(g_1, h_1) → S
  39. Segment(R, Q) → i_1
  40. Segment(S, P) → j_1
  41. Intersect(i_1, j_1) → T
  42. Rotate(P, (-α), T) → P'
  43. Rotate(R, (-α), T) → R'
  44. Rotate(S, (-α), T) → S'
  45. Rotate(Q, (-α), T) → Q'
  46. Polygon(P', R', S', Q') → poly4', p', r', s', q'
  47. Segment(U, V) → t_1
  48. Line(W, t_1) → b_2
  49. Point(b_2) → Z
  50. Segment(W, V) → d_2
  51. Segment(Z, U) → e_2
  52. Intersect(d_2, e_2) → A_1
  53. Rotate(U, (-α), A_1) → U'
  54. Rotate(V, (-α), A_1) → V'
  55. Rotate(Z, (-α), A_1) → Z'
  56. Rotate(W, (-α), A_1) → W'
  57. Line(B_1, C_1) → f_2
  58. Mirror(D_1, f_2) → E_1
  59. Segment(D_1, E_1) → g_2
  60. Intersect(f_2, g_2) → F_1
  61. Rotate(D_1, (-α), F_1) → G_1
  62. Rotate(B_1, (-α), F_1) → H_1
  63. Rotate(E_1, (-α), F_1) → I_1
  64. Rotate(C_1, (-α), F_1) → J_1
  65. Polygon(G_1, H_1, I_1, J_1) → poly6', g_3, h_2, i_2, j_2
  66. Rotate(poly2, (-α), J) → poly2'
  67. Intersect(h, i) → L_1
  68. PointIn(poly2') → K_1