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Isosceles Triangles: Examples and Non-Examples

Isosceles Triangles: Examples and Non-Examples
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2015-07-17 06:37
TriangleAngleGeometric Construction
This example demonstrates the construction and properties of isosceles triangles using GeoGebra. Key mathematical concepts include triangle classification, angle bisectors, and properties of isosceles triangles. Construction involves commands like Rotate, Angle, Segment, Point, and tools such as Midpoint and Circle. Suitable for middle school students learning geometric constructions or for educational demonstrations.

GeoGebra Commands & Parameters

  1. Rotate(A, 36*°, B) → A'
  2. Angle(A, B, A') → α
  3. Segment(C, D) → a
  4. Rotate(C, α, D) → C'
  5. Rotate(D, α, D) → D'
  6. Segment(C', D') → a'
  7. Point(a') → E
  8. Ray(D, E) → b
  9. Point(b) → F
  10. Segment(C, F) → c
  11. AngularBisector(C, D, F) → d
  12. Intersect(d, c) → G
  13. Segment(D, G) → e
  14. Segment(D, F) → f
  15. Angle(C, D, G) → β
  16. Angle(G, D, F) → γ
  17. Segment(H, I) → g
  18. Segment(H, J) → h
  19. Mirror(H, g) → H'
  20. Mirror(J, g) → J'
  21. Segment(H', J') → h'
  22. Segment(J, J') → i
  23. Angle(J', J, H) → δ
  24. Angle(H, J', J) → ε
  25. Segment(K, L) → j
  26. Segment(L, M) → k
  27. Segment(M, K) → l
  28. OrthogonalLine(L, l) → m
  29. Intersect(m, l) → N
  30. Segment(L, N) → n
  31. Angle(M, N, L) → ζ
  32. Point(Circle[O, 2.5]) → P
  33. Segment(O, P) → p
  34. Midpoint(O, P) → Q
  35. Segment(O, R) → q
  36. Segment(R, P) → r
  37. Segment(R, Q) → s
  38. Segment(S, T) → t
  39. Midpoint(S, T) → U
  40. OrthogonalLine(U, t) → a_1
  41. Point(a_1) → V
  42. Segment(S, V) → b_1
  43. Segment(V, T) → c_1
  44. Segment(V, U) → d_1
  45. Segment(W, Z) → e_1
  46. Midpoint(e_1) → A_1
  47. OrthogonalLine(A_1, e_1) → f_1
  48. Point(f_1) → B_1
  49. Segment(W, B_1) → g_1
  50. Segment(B_1, Z) → h_1
  51. Point(f_1) → C_1
  52. Point(f_1) → D_1
  53. Segment(C_1, D_1) → i_1
  54. Segment(E_1, F_1) → j_1
  55. Circle(G_1, 0.3) → k_1
  56. Midpoint(S, U) → H_1
  57. Point(k_1) → J_1
  58. Segment(G_1, J_1) → l_1
  59. Circle(H_1, l_1) → p_1
  60. OrthogonalLine(H_1, t) → m_1
  61. Intersect(p_1, m_1, 2) → K_1
  62. Intersect(p_1, m_1, 1) → L_1
  63. Segment(S, U) → q_1
  64. Segment(U, T) → r_1
  65. Midpoint(F_1, E_1) → I_1
  66. OrthogonalLine(I_1, j_1) → n_1
  67. Segment(F_1, I_1) → s_1
  68. Segment(I_1, E_1) → t_1
  69. Segment(E_1, M_1) → a_2
  70. Segment(M_1, F_1) → b_2
  71. Point(n_1) → N_1
  72. Point(n_1) → O_1
  73. Segment(N_1, O_1) → c_2
  74. Angle(F_1, I_1, O_1) → η
  75. Rotate(A_2, 36*°, B_2) → A'_1
  76. Angle(A_2, B_2, A'_1) → α_1
  77. Segment(C_2, D_2) → a_3
  78. Rotate(C_2, α_1, D_2) → C'_1
  79. Rotate(D_2, α_1, D_2) → D'_1
  80. Segment(C'_1, D'_1) → a'_1
  81. Point(a'_1) → E_2
  82. Ray(D_2, E_2) → b_3
  83. Point(b_3) → F_2
  84. Segment(C_2, F_2) → c_3
  85. AngularBisector(C_2, D_2, F_2) → d_2
  86. Intersect(d_2, c_3) → G_2
  87. Segment(D_2, G_2) → e_2
  88. Segment(D_2, F_2) → f_2
  89. Angle(C_2, D_2, G_2) → β_1
  90. Angle(G_2, D_2, F_2) → γ_1
  91. OrthogonalLine(C_2, e_2) → g_2
  92. Intersect(g_2, f_2) → P_1
  93. Segment(D_2, P_1) → h_2
  94. Midpoint(C_2, P_1) → Q_1
  95. Segment(C_2, P_1) → i_2
  96. Segment(Q_1, D_2) → j_2
  97. Angle(P_1, Q_1, D_2) → θ
  98. Angle(T, U, V) → ι