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Similar Triangles Demo by olperocchi02

Similar Triangles Demo by olperocchi02
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2018-01-02 21:14
TriangleTransformationGeometric Construction
This example demonstrates the properties and criteria of similar triangles. It involves core math concepts like triangle similarity, geometric transformations, and linear equations. Construction highlights include using GeoGebra commands such as Mirror, Ray, Point, Line, Polygon, Intersect, Segment, Dilate, OrthogonalLine, and Angle. Suitable for high school mathematics teaching or for geometry enthusiasts.

GeoGebra Commands & Parameters

  1. Mirror(G, F) → G'
  2. Ray(F, G') → l
  3. Point(l) → J
  4. Line(H, F) → n_2
  5. Polygon(F, G, H) → poly2, h_1, f_3, g_1
  6. Line(J, f_3) → q_2
  7. Intersect(n_2, q_2) → A_1
  8. Line(A, B) → b_1
  9. Polygon(C, A, B) → poly1, b, c, a_2
  10. Ray(A, C) → g
  11. Point(g) → D
  12. Line(D, a_2) → l_2
  13. Intersect(b_1, l_2) → Z
  14. Ray(A, B) → f
  15. Segment(D, A) → h
  16. Segment(E, A) → i
  17. Segment(D, E) → j
  18. Mirror(H, F) → H'
  19. Ray(F, H') → k
  20. Segment(I, F) → m
  21. Segment(F, J) → n
  22. Segment(J, I) → p
  23. Polygon(A, D, E) → poly3, e, a_1, d
  24. Polygon(F, J, I) → poly4, i_1, f_2, j_1
  25. Polygon(K, L, M) → poly5, m_1, k_1, l_1
  26. Dilate(M, o, M) → M'
  27. Dilate(K, o, Scale) → K'
  28. Dilate(L, o, Scale) → L'
  29. Dilate(M, o, Scale) → M'_1
  30. Polygon(K', L', M'_1) → poly5', m'_1, k', l'
  31. Segment(O, P) → q
  32. Segment(O, Q) → r
  33. Segment(P, Q) → s
  34. Dilate(O, 1 / 3, Q) → O'
  35. Line(O', s) → t
  36. Intersect(q, t) → R
  37. Segment(R, O') → n_1
  38. Segment(O, O') → p_1
  39. Segment(O', Q) → q_1
  40. Segment(R, P) → r_1
  41. Segment(R, O) → s_1
  42. Line(A, C) → t_1
  43. Line(F, p) → c_1
  44. Line(G, m) → d_1
  45. Intersect(d_1, c_1) → S
  46. Segment(T, U) → e_1
  47. OrthogonalLine(T, e_1) → g_2
  48. Point(g_2) → V
  49. Segment(V, U) → h_2
  50. Segment(T, V) → i_2
  51. OrthogonalLine(T, h_2) → j_2
  52. Intersect(h_2, j_2) → W
  53. Segment(W, U) → k_2
  54. Segment(W, V) → m_2
  55. Segment(W, T) → p_2
  56. Angle(T, V, W) → α
  57. Angle(W, U, T) → β
  58. Angle(T, W, V) → γ
  59. Angle(T, W, U) → δ
  60. Angle(U, T, W) → ε
  61. Angle(W, T, V) → ζ
  62. Angle(A_1, F, J) → η
  63. Angle(G, F, H) → θ
  64. Angle(F, A_1, J) → ι
  65. Angle(A_1, J, F) → κ
  66. Angle(F, G, H) → λ
  67. Angle(F, H, G) → μ