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From Hexagon to Triangle

From Hexagon to Triangle
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2023-03-13 17:53
TrianglePolygonTransformationGeometric Construction
In collections geometriadinamica.es
This GeoGebra example demonstrates how to transform a hexagon into a triangle. The core mathematical concepts involved include geometric transformations and similarity. The construction involves using GeoGebra commands such as Circle, Intersect, Mirror, Polygon, etc. to create the hexagon and triangle graphs. This example is suitable for middle school or high school students learning geometric transformations and similarity.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Circle(B, A) → d
  3. Intersect(c, d) → C, D, ,
  4. Mirror(C, A) → E
  5. Mirror(D, A) → F
  6. Mirror(B, A) → G
  7. Polygon(E, G, F, C, B, D) → P, e, g, f, c_1, b, d_1
  8. Polygon(F, A, C) → Q, c_2, f_1, a
  9. Mirror(E, G) → H
  10. OrthogonalLine(H, e) → h
  11. Midpoint(A, F) → I
  12. OrthogonalLine(G, e) → i
  13. Circle(G, H) → k
  14. Intersect(k, i) → J, K
  15. Circle(H, J) → p
  16. Circle(G, I) → q
  17. Intersect(p, h, 1) → L
  18. Segment(L, E) → j
  19. Intersect(q, i, 2) → M
  20. OrthogonalLine(M, i) → l
  21. Intersect(l, j) → N
  22. Segment(N, D) → m
  23. Intersect(e, m) → O
  24. Segment(G, H) → n
  25. Intersect(q, n) → R,
  26. Circle(I, R) → r
  27. Intersect(r, m) → S, T
  28. Intersect(r, c_1) → U,
  29. Polygon(I, F, G, O, T) → V, i_1, f_2, g_1, o, t
  30. Polygon(O, D, E) → W, e_1, o_1, d_2
  31. Polygon(U, B, D, T) → Y, u, b_1, d_3, t_1
  32. Polygon(U, T, I, A, C) → Z, u_1, t_2, i_2, a_1, c_3
  33. Rotate(O, (-aa), O) → O'
  34. Rotate(D, (-aa), O) → D'
  35. Rotate(E, (-aa), O) → E'
  36. Polygon(O', D', E') → W', e', o', d'
  37. Rotate(U, (-aa), O) → U'
  38. Rotate(B, (-aa), O) → B'
  39. Rotate(D, (-aa), O) → D'_1
  40. Rotate(T, (-aa), O) → T'
  41. Polygon(U', B', D'_1, T') → Y', u', b', d'_1, t'
  42. Mirror(E, O) → A_1
  43. Midpoint(A_1, F) → B_1
  44. Rotate(F, (-aa), B_1) → F'
  45. Rotate(A, (-aa), B_1) → A'
  46. Rotate(C, (-aa), B_1) → C'
  47. Polygon(F', A', C') → Q', c', f', a'
  48. Rotate(U', (-aa), D'_1) → U''
  49. Rotate(B', (-aa), D'_1) → B''
  50. Rotate(D'_1, (-aa), D'_1) → D'_1'
  51. Rotate(T', (-aa), D'_1) → T''
  52. Polygon(U'', B'', D'_1', T'') → Y'', u'', b'', d'_1', t''
  53. Rotate(U, aa, I) → U'_1
  54. Rotate(T, aa, I) → T'_1
  55. Rotate(I, aa, I) → I'
  56. Rotate(A, aa, I) → A'_1
  57. Rotate(C, aa, I) → C'_1
  58. Polygon(U'_1, T'_1, I', A'_1, C'_1) → Z', u'_1, t'_1, i', a'_1, c'_1
  59. Vector(C_1, D_1) → v

AI Drawing Prompt Reference

Draw a triangle transformed from a hexagon. First, draw two circles to find intersection points C and D, then mirror C and D to get E and F, and mirror B to get G. Use E, G, F, C, B, and D to draw hexagon P. Next, draw triangle Q with F, A, and C, then mirror E and G to get H, draw the perpendicular line h from H, find midpoint I, draw circle k with G and H, find intersection points J and K, continue to draw circles p and q, find intersection points L and M, draw N, and finally draw triangle W with O, D, and E.
The prompt above was compiled from the original drawing commands and is for reference only.