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Similar Triangles Demo by elkane01

Similar Triangles Demo by elkane01
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2018-01-03 01:39
TriangleAngleGeometric Construction
This example demonstrates the properties and criteria of similar triangles, visually showing the relationships of corresponding equal angles and proportional sides through dynamic geometry. It involves core math concepts like similarity criteria, proportional segments, angle measurement, and geometric transformations. Constructed using GeoGebra commands such as Line, Polygon, Ray, Point, Intersect, Mirror, Dilate, OrthogonalLine, Angle, Perimeter, and PointIn. Suitable for high school geometry teaching to help students intuitively understand similar triangles and develop spatial reasoning skills.

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) → l_2
  6. Intersect(b_1, l_2) → A_1
  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. Point(e_1) → W
  47. Segment(V, W) → h_2
  48. Segment(W, T) → i_2
  49. Segment(T, V) → j_2
  50. OrthogonalLine(T, h_2) → k_2
  51. Intersect(h_2, k_2) → Z
  52. Angle(T, V, Z) → α
  53. Angle(V, Z, T) → β
  54. Angle(T, W, Z) → γ
  55. Angle(T, Z, W) → δ
  56. Angle(W, T, Z) → ε
  57. Angle(V, T, Z) → ζ
  58. Angle(poly3) → η, θ, ι
  59. Angle(poly3) → κ, λ, μ
  60. Angle(poly3) → ν, ξ, ο
  61. Angle(A, B, C) → ρ
  62. Angle(B, C, A) → σ
  63. Perimeter(poly3) → perimeterpoly3
  64. PointIn(poly3) → Pointpoly3_1
  65. Perimeter(poly3) → u
  66. PointIn(poly3) → Pointpoly3
  67. Line(I, f_1) → m_2