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Rotational Symmetry Demo by Adam Normand

Rotational Symmetry Demo by Adam Normand
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2017-10-01 12:57
PolygonAngleTransformationGeometric Construction
This example demonstrates the rotational symmetry of polygons rotating around a central point. Key math concepts include rotational symmetry, central symmetry, angles, and polygon construction. It uses commands like Polygon, Midpoint, Segment, Intersect, Rotate, Angle, and Point in GeoGebra. Suitable for high school students learning geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, a, a_1, b, C
  2. Midpoint(a) → D
  3. Midpoint(a_1) → E
  4. Segment(A, E) → c
  5. Segment(D, C) → d
  6. Intersect(c, d) → F
  7. Rotate(A, α, F) → A'
  8. Rotate(B, α, F) → B'
  9. Rotate(C, α, F) → C'
  10. Polygon(A', B', C') → poly1', c', a', b'
  11. Polygon(G, H, I, J) → poly2, g, h, i, j
  12. Segment(G, I) → e
  13. Segment(J, H) → f
  14. Intersect(e, f) → K
  15. Rotate(G, α, K) → G'
  16. Rotate(H, α, K) → H'
  17. Rotate(I, α, K) → I'
  18. Rotate(J, α, K) → J'
  19. Polygon(G', H', I', J') → poly2', g', h', i', j'
  20. Polygon(M, N, 5) → poly3, m_1, n, p, q, r, O, P, Q
  21. Midpoint(p) → R
  22. Midpoint(n) → S
  23. Segment(Q, S) → s
  24. Segment(M, R) → t
  25. Intersect(t, s) → T
  26. Rotate(M, α, T) → M'
  27. Rotate(N, α, T) → N'
  28. Rotate(O, α, T) → O'
  29. Rotate(P, α, T) → P'
  30. Rotate(Q, α, T) → Q'
  31. Polygon(M', N', O', P', Q') → poly3', m', n', o', p', q'
  32. Angle(B, A, C) → β
  33. Angle(B', A', C') → γ
  34. Angle(H, G, J) → δ
  35. Angle(H', G', J') → ε
  36. Segment(G', I') → b_1
  37. Segment(J', H') → c_1
  38. Intersect(c_1, b_1) → U
  39. Angle(N', M', Q') → ζ
  40. Angle(N, M, Q) → η
  41. Segment(T, M') → d_1
  42. Point(d_1) → V
  43. Segment(V, N') → e_1
  44. Segment(V, O') → f_1
  45. Segment(V, P') → g_1
  46. Segment(V, Q') → h_1
  47. Polygon(W, Z, 4) → poly4, i_1, j_1, k_1, l_1, A_1, S'
  48. Rotate(poly4, α, C_1) → poly4'

AI Drawing Prompt Reference

Draw an equilateral triangle ABC and rotate it around point F to create a rotational symmetry figure A'B'C'. Then, draw a quadrilateral GHIJ and rotate it around point K to create another rotational symmetry figure G'H'I'J'. Next, draw a pentagon MNPQR and rotate it around point T to create a rotational symmetry figure M'N'O'P'Q'. Finally, measure angles β, γ, δ, ε, and draw auxiliary lines b1, c1, d1, e1, f1, g1, h1 to create the final quadrilateral WZ.
The prompt above was compiled from the original drawing commands and is for reference only.