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Shearer Action 4! Geometric Construction and Symmetry

Shearer Action 4! Geometric Construction and Symmetry
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2019-05-04 10:08
CircleVectorGeometric Construction
This example demonstrates solving geometric problems using dynamic tools. Key mathematical concepts include circles, vectors, centroid or barycenter, and Pythagorean theorem. Construction involves GeoGebra commands like Ray, Point, Circle, and OrthogonalLine. Suitable for middle school geometry learners to understand transformations and symmetry.

GeoGebra Commands & Parameters

  1. Ray(A, A + (0, 1)) → f
  2. Point(f) → B
  3. Circle(B, A) → c
  4. Ray(A, A + (2, 0)) → h
  5. Point(h) → C
  6. Point(c) → F
  7. Segment(B, F) → j
  8. OrthogonalLine(F, j) → l
  9. Line(B, F) → m
  10. Intersect(g, l) → G
  11. Angle(C, G, F) → α
  12. Rotate(C, α / 2, G) → C'
  13. Ray(G, C') → n
  14. Intersect(m, n) → H
  15. Circle(H, F) → d
  16. Intersect(d, g, 1) → D
  17. CircleArc(B, F, A) → e
  18. CircleArc(H, D, F) → k
  19. Point(e) → E
  20. Point(k) → I
  21. Angle(A, E, F) → β
  22. Angle(F, I, D) → γ
  23. Midpoint(A, D) → J
  24. Ray(J, J - (0, 1)) → i
  25. Point(i) → K
  26. Angle(A, J, K) → ε
  27. Point(g) → L
  28. Point(g) → M
  29. Angle(M, D, H) → ζ
  30. Angle(B, A, L) → η
  31. Segment(H, D) → q
  32. Segment(B, A) → p
  33. Dilate(B, If[0 < b ≤ 1, 1 - b, 0], A) → B'
  34. Dilate(H, If[0 < b ≤ 1, 1 - b, 0], D) → H'
  35. Segment(B, B') → r
  36. Segment(H, H') → s
  37. Dilate(E, If[1 < b ≤ 2, 2 - b, 0], A) → E'
  38. Dilate(E, If[1 < b ≤ 2, 2 - b, 0], F) → E'_1
  39. Dilate(I, If[1 < b ≤ 2, 2 - b, 0], F) → I'
  40. Dilate(I, If[1 < b ≤ 2, 2 - b, 0], D) → I'_1
  41. Segment(E, E') → t
  42. Segment(E, E'_1) → f_1
  43. Segment(I, I') → g_1
  44. Segment(I, I'_1) → h_1
  45. Min({Distance[E, A], Distance[E, F], Distance[I, F], Distance[I, D]}) → o
  46. Circle(E, (0.3 * o)) → c_1
  47. Circle(I, (0.3 * o)) → d_1
  48. Intersect(c_1, t, 1) → N
  49. Intersect(d_1, g_1, 1) → O
  50. Rotate(O, If[2 < b ≤ 3, ((b - 2) * γ), γ], I) → O'
  51. Rotate(N, If[2 < b ≤ 3, ((b - 2) * β), β], E) → N'
  52. CircleSector(E, N, N') → e_1
  53. CircleSector(I, O, O') → k_1
  54. Line(E, i) → i_1
  55. Point(i_1) → P
  56. Angle(P, E, A) → θ
  57. Semicircle(E, J) → p_1
  58. Rotate(E, If[4 < b ≤ 5, ((-(b - 4)) * π), (-π)], Midpoint[E, J]) → E'_2
  59. Vector(E, E'_2) → u
  60. Translate(e_1, u) → q_1
  61. Rotate(q_1, If[4 < b ≤ 5, ((b - 4) * ((2 * π) - θ)), (2 * π) - θ], E'_2) → r_1
  62. Semicircle(J, I) → s_1
  63. Dilate(I, If[5 < b ≤ 6, 6 - b, 0], J) → I'_2
  64. Vector(I, I'_2) → v
  65. Translate(k_1, v) → t_1
  66. Line(I, g) → j_1
  67. Point(j_1) → Q
  68. Angle(D, I, Q) → κ
  69. Rotate(t_1, If[5 < b ≤ 6, ((-(b - 5)) * ((2 * π) - κ)), κ - (2 * π)], I'_2) → c_2