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Rotational Symmetry Demo

Rotational Symmetry Demo
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2019-06-21 02:05
PolygonTransformationGeometric Construction
This example demonstrates the concept of rotational symmetry in geometry. It involves core math concepts such as symmetry, rotation, angles, and polygon construction. The construction uses GeoGebra commands like Corner, Midpoint, Polygon, Segment, Intersect, Rotate, Angle, and Point. Suitable for high school geometry teaching to understand and apply the concept of rotational symmetry.

GeoGebra Commands & Parameters

  1. Corner(pic1, 1) → LB
  2. Midpoint(LB, RT) → MM
  3. Polygon(A, B, 3) → poly1, a, a_1, b, C
  4. Midpoint(a) → D
  5. Midpoint(a_1) → E
  6. Segment(A, E) → c
  7. Segment(D, C) → d
  8. Intersect(c, d) → F
  9. Rotate(A, α, F) → A'
  10. Rotate(B, α, F) → B'
  11. Rotate(C, α, F) → C'
  12. Polygon(A', B', C') → poly1', c', a', b'
  13. Polygon(G, H, I, J) → poly2, g, h, i, j
  14. Segment(G, I) → e
  15. Segment(J, H) → f
  16. Intersect(e, f) → K
  17. Rotate(G, α, K) → G'
  18. Rotate(H, α, K) → H'
  19. Rotate(I, α, K) → I'
  20. Rotate(J, α, K) → J'
  21. Polygon(G', H', I', J') → poly2', g', h', i', j'
  22. Rotate(pic1, α, L) → pic1'
  23. Polygon(M, N, 5) → poly3, m_1, n, p, q, r, O, P, Q
  24. Midpoint(p) → R
  25. Midpoint(n) → S
  26. Segment(Q, S) → s
  27. Segment(M, R) → t
  28. Intersect(t, s) → T
  29. Rotate(M, α, T) → M'
  30. Rotate(N, α, T) → N'
  31. Rotate(O, α, T) → O'
  32. Rotate(P, α, T) → P'
  33. Rotate(Q, α, T) → Q'
  34. Polygon(M', N', O', P', Q') → poly3', m', n', o', p', q'
  35. Angle(B, A, C) → β
  36. Angle(B', A', C') → γ
  37. Angle(H, G, J) → δ
  38. Angle(H', G', J') → ε
  39. Segment(G', I') → b_1
  40. Segment(J', H') → c_1
  41. Intersect(c_1, b_1) → U
  42. Angle(N', M', Q') → ζ
  43. Angle(N, M, Q) → η
  44. Segment(T, M') → d_1
  45. Point(d_1) → V
  46. Segment(V, N') → e_1
  47. Segment(V, O') → f_1
  48. Segment(V, P') → g_1
  49. Segment(V, Q') → h_1
  50. Corner(pic1, 2) → RB

AI Drawing Prompt Reference

Draw a figure with rotational symmetry. Start by constructing triangle ABC, then rotate it around point F to form triangle A'B'C'. Next, construct another triangle GHIJ and rotate it around point K to form G'H'I'J'. Finally, rotate the entire figure around point T to form the new polygon M'N'O'P'Q'. Pay attention to the angle and rotation center to ensure the figure has rotational symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.