Definition of Symmetry Rules

Definition of Symmetry Rules
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2019-06-18 09:56
This example illustrates the concept of symmetry rules. It involves symmetry in geometric transformations using basic geometric concepts like rotation and angles. Commands used include Circle, Point, Segment, Rotate, Angle, and PointIn. Suitable for middle school and above students to learn about geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Circle(A, a) → c
  2. Point(c) → B
  3. Segment(B, A) → f
  4. Rotate(B, 18°, A) → B'
  5. Angle(B, A, B') → α
  6. Rotate(B', 18°, A) → B''
  7. Angle(B', A, B'') → β
  8. Rotate(B'', 18°, A) → B'''
  9. Angle(B'', A, B''') → γ
  10. Rotate(B''', 18°, A) → C
  11. Angle(B''', A, C) → δ
  12. Rotate(C, 18°, A) → C'
  13. Angle(C, A, C') → ε
  14. Rotate(C', 18°, A) → C''
  15. Angle(C', A, C'') → ζ
  16. Rotate(C'', 18°, A) → C'''
  17. Angle(C'', A, C''') → η
  18. Rotate(C''', 18°, A) → D
  19. Angle(C''', A, D) → θ
  20. Rotate(D, 18°, A) → D'
  21. Angle(D, A, D') → ι
  22. Rotate(D', 18°, A) → D''
  23. Angle(D', A, D'') → κ
  24. Rotate(D'', 18°, A) → D'''
  25. Angle(D'', A, D''') → λ
  26. Rotate(D''', 18°, A) → E
  27. Angle(D''', A, E) → μ
  28. Rotate(E, 18°, A) → E'
  29. Angle(E, A, E') → ν
  30. Rotate(E', 18°, A) → E''
  31. Angle(E', A, E'') → ξ
  32. Rotate(E'', 18°, A) → E'''
  33. Angle(E'', A, E''') → ο
  34. Rotate(E''', 18°, A) → F
  35. Angle(E''', A, F) → ρ
  36. Rotate(F, 18°, A) → F'
  37. Angle(F, A, F') → σ
  38. Rotate(F', 18°, A) → F''
  39. Angle(F', A, F'') → τ
  40. Rotate(F'', 18°, A) → F'''
  41. Angle(F'', A, F''') → υ
  42. Segment(B, D''') → g
  43. Segment(F''', D''') → h
  44. Segment(F'', D''') → i
  45. Segment(F', D''') → j
  46. Segment(F, D''') → k
  47. Segment(E'', D''') → l
  48. Segment(E', D''') → m
  49. Segment(E, D''') → n
  50. Segment(D''', D''') → p
  51. Segment(D'', D''') → q
  52. Segment(D', D''') → r
  53. Segment(D, D''') → s
  54. Segment(C''', D''') → t
  55. Segment(C'', D''') → b
  56. Segment(C', D''') → d
  57. Segment(C, D''') → e
  58. Segment(B''', D''') → f_1
  59. Segment(B'', D''') → g_1
  60. Segment(B', D''') → h_1
  61. Segment(E''', D''') → i_1
  62. PointIn(c) → Pointc
  63. Segment(I, J) → j_1

AI Drawing Prompt Reference

Draw a circle c, then take point B on the circle and connect BA. Next, rotate point B around A by 18 degrees to form points B', B'', B''', etc. Connect adjacent points to form a polygon. Finally, connect B to D''', F''' to D''', F'' to D''', F' to D''', F to D''', E'' to D''', E' to D''', E to D''', D'' to D''', D' to D''', D to D''', D''' to D'', D'' to D'', D' to D'', D to D'', E''' to D', E'' to D', E' to D', E to D', F''' to D', F'' to D', F' to D', F to D', E''' to D.
The prompt above was compiled from the original drawing commands and is for reference only.