Similar Triangles by famirchi00

Similar Triangles by famirchi00
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2018-01-02 21:15
This example illustrates the properties of similar triangles, involving corresponding angles and proportional sides. Using GeoGebra commands such as Line, Polygon, and Dilate, the construction process of similar triangles is dynamically demonstrated. Suitable for middle and high school students learning about similar triangles.

GeoGebra Commands & Parameters

  1. Line(A, B) → b_1
  2. Polygon(C, A, B) → poly1, b, c, a_2
  3. Ray(A, C) → g
  4. Point(g) → D
  5. Line(D, a_2) → r_2
  6. Intersect(b_1, r_2) → Z
  7. Mirror(G, F) → G'
  8. Ray(F, G') → l
  9. Point(l) → J
  10. Polygon(F, G, H) → poly2, h_1, f_1, g_1
  11. Ray(A, B) → f
  12. Segment(D, A) → h
  13. Segment(E, A) → i
  14. Segment(D, E) → j
  15. Mirror(H, F) → H'
  16. Ray(F, H') → k
  17. Segment(I, F) → m
  18. Segment(F, J) → n
  19. Segment(J, I) → p
  20. Polygon(A, D, E) → poly3, e, a_1, d
  21. Polygon(F, J, I) → poly4, i_1, f_2, j_1
  22. Polygon(K, L, M) → poly5, m_1, k_1, l_1
  23. Dilate(M, o, M) → M'
  24. Dilate(K, o, Scale) → K'
  25. Dilate(L, o, Scale) → L'
  26. Dilate(M, o, Scale) → M'_1
  27. Polygon(K', L', M'_1) → poly5', m'_1, k', l'
  28. Segment(O, P) → q
  29. Segment(O, Q) → r
  30. Segment(P, Q) → s
  31. Dilate(O, 1 / 3, Q) → O'
  32. Line(O', s) → t
  33. Intersect(q, t) → R
  34. Segment(R, O') → n_1
  35. Segment(O, O') → p_1
  36. Segment(O', Q) → q_1
  37. Segment(R, P) → r_1
  38. Segment(R, O) → s_1
  39. Line(A, C) → t_1
  40. Line(F, p) → c_1
  41. Line(G, m) → d_1
  42. Intersect(d_1, c_1) → S
  43. Line(T, U) → e_1
  44. OrthogonalLine(T, e_1) → g_2
  45. Point(g_2) → V
  46. Line(V, U) → h_2
  47. LineBisector(U, V) → i_2
  48. Intersect(h_2, i_2) → W
  49. Line(T, W) → j_2
  50. Segment(V, T) → k_2
  51. Segment(T, U) → l_2
  52. Segment(U, W) → m_2
  53. Segment(W, V) → n_2
  54. Line(T, V) → p_2
  55. Segment(T, W) → q_2
  56. Angle(T, V, W) → α
  57. Angle(V, W, T) → β
  58. Angle(W, T, V) → γ
  59. Angle(W, T, U) → δ
  60. Angle(U, W, T) → ε
  61. Angle(T, U, W) → ζ
  62. Angle(C, B, A) → η
  63. Angle(D, Z, A) → θ
  64. Angle(A, C, B) → ι
  65. Angle(B, A, C) → κ
  66. Angle(Z, E, D) → λ
  67. Angle(Z, E, D) → μ
  68. Angle(Z, E, D) → ν
  69. Angle(Z, E, D) → ξ
  70. Angle(D, Z, E) → ο
  71. Angle(Z, E, D) → ρ

AI Drawing Prompt Reference

Draw two similar triangles by first creating triangle ABC, then drawing a ray from A through C, taking point D on the ray, connecting AD and DE, and using reflections and rotations to create similar triangles DEF and GHI. Finally, use the line segments AD and DE to construct the similar triangles.
The prompt above was compiled from the original drawing commands and is for reference only.