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Symmetry - 'Create Your Own' Example

Symmetry - 'Create Your Own' Example
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2015-07-01 00:15
Coordinate GeometryGeometric Construction
This example demonstrates the creation of reflective and rotational symmetry figures. It involves core math concepts like symmetry, special points, congruence, expected value, parabola, and inequalities. Construction uses GeoGebra commands such as Circle, Line, Segment, Point, Polygon, Rotate, and Mirror. Suitable for high school mathematics instruction or student exploration of symmetry principles.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Line(A, B) → a
  3. Segment(B, C) → b
  4. Point(c) → D
  5. Segment(C, D) → d
  6. Polygon(D, C, B) → poly1, b_1, d_1, c_1
  7. Rotate(B, 30*°, A) → B'
  8. Rotate(B, 30*°, A) → B'_1
  9. Rotate(D, -30*°, A) → D'
  10. Rotate(C, -30*°, A) → C'
  11. Rotate(B, -30*°, A) → B'_2
  12. Polygon(D', C', B'_2) → poly1', b'_2, d', c'
  13. Rotate(D', -30*°, A) → D''
  14. Rotate(C', -30*°, A) → C''
  15. Rotate(B'_2, -30*°, A) → E
  16. Polygon(D'', C'', E) → poly1'', e, d'', c''
  17. Rotate(D'', -30*°, A) → D'''
  18. Rotate(C'', -30*°, A) → C'''
  19. Rotate(E, -30*°, A) → E'
  20. Polygon(D''', C''', E') → poly1''', e', d''', c'''
  21. Rotate(D''', -30*°, A) → F
  22. Rotate(C''', -30*°, A) → G
  23. Rotate(E', -30*°, A) → E''
  24. Polygon(F, G, E'') → poly2, e'', f, g
  25. Rotate(F, -30*°, A) → F'
  26. Rotate(G, -30*°, A) → G'
  27. Rotate(E'', -30*°, A) → E'''
  28. Polygon(F', G', E''') → poly2', e''', f', g'
  29. Mirror(D, a) → D'_1
  30. Mirror(C, a) → C'_1
  31. Mirror(B, a) → B'_3
  32. Polygon(D'_1, C'_1, B'_3) → poly1'_1, b'_3, d'_1, c'_1
  33. Mirror(D', a) → D''_1
  34. Mirror(C', a) → C''_1
  35. Mirror(B'_2, a) → H
  36. Polygon(D''_1, C''_1, H) → poly1''_1, h, d''_1, c''_1
  37. Mirror(D'', a) → D'''_1
  38. Mirror(C'', a) → C'''_1
  39. Mirror(E, a) → E'_1
  40. Polygon(D'''_1, C'''_1, E'_1) → poly1'''_1, e'_1, d'''_1, c'''_1
  41. Mirror(D''', a) → I
  42. Mirror(C''', a) → J
  43. Mirror(E', a) → E''_1
  44. Polygon(I, J, E''_1) → poly3, e''_1, i, j
  45. Mirror(F, a) → F'_1
  46. Mirror(G, a) → G'_1
  47. Mirror(E'', a) → E'''_1
  48. Polygon(F'_1, G'_1, E'''_1) → poly2'_1, e'''_1, f'_1, g'_1
  49. Mirror(F', a) → F''
  50. Mirror(G', a) → G''
  51. Mirror(E''', a) → K
  52. Polygon(F'', G'', K) → poly2'', k, f'', g''
  53. Mirror(B, a) → B'_4
  54. Mirror(C, a) → C'_2
  55. Segment(B'_4, C'_2) → b'
  56. Mirror(C, a) → C'_3
  57. Mirror(D, a) → D'_2
  58. Segment(C'_3, D'_2) → d'_2
  59. Mirror(A, a) → A'

AI Drawing Prompt Reference

Draw a symmetric figure with a circle and a line segment as the axis of symmetry. Construct a polygon and then rotate it around a vertex by 30 degrees, repeating the process. Reflect the shapes across the axis to create symmetrical patterns, demonstrating the principles of rotational and reflective symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.