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Rotational Symmetry of a Square by youngcar

Rotational Symmetry of a Square by youngcar
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2016-06-01 10:18
PolygonAngleTransformationGeometric Construction
This example demonstrates the rotational symmetry of a square: rotating the square about its center by 90°, 180°, and 270° maps it onto itself. Core mathematical concepts include properties of squares, rotation transformations, symmetry axes and centers, and angle measurement. Construction highlights: the figure is built with GeoGebra commands Segment, OrthogonalLine, Point, Intersect, Polygon, Circle, Line, Rotate, Mirror, and PointIn, creating vertices A, B, C, D, center O, their rotated images A', B', C', D', and auxiliary objects such as polygon poly2, circles, and lines. Suitable for middle‑school geometry lessons on rotational symmetry, high‑school geometric construction practice, or teacher‑created instructional material.

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

AI Drawing Prompt Reference

Draw a square that maps onto itself when rotated by 90°, 180°, and 270°. The figure includes the four vertices A, B, C, D, the center O, and the rotated vertices A', B', C', D'. Add auxiliary circles and lines to highlight symmetry. The construction order is to draw the square and center first, then rotate the vertices, and finally add auxiliary elements to emphasize symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.