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Solving Similar Triangles

Solving Similar Triangles
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2016-04-04 11:31
TriangleTrigonometryGeometric Construction
In collections Similar Triangles Review
This example demonstrates the construction and analysis of similar triangles using GeoGebra. It involves core mathematical concepts such as the criteria and properties of similar triangles, trigonometric function applications, angle measurement, and segment ratio relationships. The construction utilizes commands and objects like Circle, Point, Ray, Polygon, Intersect, Line, Segment, Angle, OrthogonalLine, and Midpoint. It is suitable for high school mathematics education, aiding students in visually understanding the geometric properties and problem-solving methods of similar triangles.

GeoGebra Commands & Parameters

  1. Circle(A, c) → d
  2. Circle(A, b) → e_4
  3. Point(d) → B
  4. Point(e_4) → C
  5. Ray(A, C) → a
  6. Ray(B, C) → f_4
  7. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  8. Circle(C, c' / (c / b)) → k
  9. Intersect(k, a, 1) → D
  10. Line(D, c_1) → m
  11. Intersect(m, f_4) → E
  12. Polygon(C, D, E) → poly2, e_1, c_2, d_1
  13. Segment(C, D) → p_2
  14. Circle(G, i) → q_2
  15. Circle(G, j) → t
  16. Point(q_2) → J
  17. Circle(J, g_3) → f_1
  18. Intersect(t, f_1, 1) → I
  19. Segment(J, G) → g_1
  20. Segment(G, I) → h_1
  21. Segment(I, J) → i_1
  22. Ray(G, J) → j_1
  23. Circle(J, fj) → k_1
  24. Intersect(k_1, j_1, 2) → F
  25. Circle(I, G) → p_1
  26. Intersect(p_1, i_1, 1) → H_1
  27. Circle(F, Radius[p_1]) → q_1
  28. Intersect(q_1, g_1, 1) → I_1
  29. Circle(I_1, Segment[H_1, G]) → r_1
  30. Intersect(q_1, r_1, 2) → K_1
  31. Ray(F, K_1) → l_1
  32. Ray(G, I) → m_1
  33. Intersect(l_1, m_1) → H
  34. Polygon(G, F, H) → poly3, h_2, g_2, f_2
  35. Angle(G, I, J) → α
  36. Angle(H, F, G) → β
  37. Segment(J, F) → h_{4}
  38. Point(h_{4}) → L_1
  39. Segment(F, H) → n_1
  40. Segment(I, H) → s_1
  41. Point(Circle[R, s]) → Q
  42. Segment(R, Q) → t_1
  43. Circle(Q, r) → d_2
  44. Circle(R, q_4) → e_2
  45. Intersect(d_2, e_2, 2) → S
  46. Circle(R, q') → k_2
  47. Ray(Q, S) → a_2
  48. Intersect(k_2, a_2, 1) → P
  49. Polygon(P, R, Q) → poly4, q_3, n_2, r_2
  50. Segment(R, S) → b_2
  51. Angle(R, P, S) → γ
  52. Angle(Q, R, S) → δ
  53. Segment(S, Q) → i_2
  54. Segment(P, S) → j_2
  55. Segment(R, S) → q
  56. Segment(P, S) → p
  57. Circle(M, o) → s_2
  58. Circle(M, n) → t_2
  59. Point(s_2) → N
  60. Segment(M, N) → l_2
  61. OrthogonalLine(N, l_2) → m_2
  62. Intersect(t_2, m_2, 2) → O
  63. Segment(O, M) → a_3
  64. Polygon(M, N, O) → poly5, o_1, u, n_3
  65. Ray(M, N) → b_3
  66. Circle(M, l) → c_3
  67. Point(c_3) → K
  68. OrthogonalLine(K, b_3) → d_3
  69. Intersect(d_3, b_3) → L
  70. Polygon(M, L, K) → poly6, v, w, l_3
  71. Angle(O, N, M) → ε
  72. Angle(M, L, K) → ζ
  73. Segment(L, N) → e_3
  74. Segment(N, O) → f_3
  75. Segment(F, H) → g
  76. Segment(I, H) → f
  77. Segment(C, D) → e
  78. Segment(T, U) → h_3
  79. OrthogonalLine(U, h_3) → i_3
  80. Midpoint(T, U) → V
  81. Circle(U, V) → k_3
  82. Intersect(k_3, i_3, 1) → W
  83. Polygon(T, U, W) → t1, w_1, t_3, u_1
  84. Angle(T, U, W) → η
  85. Angle(T, U, W) → θ
  86. OrthogonalLine(U, u_1) → j_3
  87. Intersect(j_3, u_1) → Z
  88. Segment(U, Z) → h
  89. Angle(U, Z, T) → ι
  90. Segment(U, Z) → m_3