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Drawing Similar Triangles

Drawing Similar Triangles
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2017-09-16 02:02
TriangleVectorGeometric Construction
This example demonstrates how to draw similar triangles. Key mathematical concepts include the properties of similar triangles and geometric mean. Using GeoGebra commands such as Point, Segment, Rotate, etc., specific angles and side lengths are constructed to form similar triangles. Suitable for middle and high school students studying similar triangles.

GeoGebra Commands & Parameters

  1. Point(Circle[B, DRAG]) → C_2
  2. Segment(B, C) → l_1
  3. Segment(B, A) → m_1
  4. Segment(C, A) → n_1
  5. Rotate(C_2, (-α), B) → B'
  6. Angle(B', B, C_2) → β
  7. Vector(B, B') → u
  8. Point(u) → X_1
  9. Circle(B, DRAG / 8) → c
  10. Point(u) → X
  11. Point(c) → C_1
  12. Point(c) → D
  13. CircleArc(B, C_1, D) → d
  14. Segment(B, B') → g
  15. Intersect(d, g, 1) → B_1
  16. Circle(B_1, DRAG / 8) → e
  17. Point(e) → F
  18. Point(e) → G
  19. CircleArc(B_1, F, G) → h
  20. Intersect(h, g) → B_2,
  21. Circle(B_2, DRAG / 8) → k
  22. Point(k) → A_1
  23. Point(k) → E
  24. CircleArc(B_2, A_1, E) → p
  25. Intersect(p, g) → B_3,
  26. Circle(B_3, DRAG / 8) → q
  27. Point(q) → I
  28. Point(q) → J
  29. CircleArc(B_3, I, J) → r
  30. Intersect(r, g, 1) → B_4
  31. Circle(B_4, DRAG / 8) → s
  32. Point(s) → K
  33. Point(s) → L
  34. CircleArc(B_4, K, L) → t
  35. Intersect(t, g) → B_5,
  36. Circle(B_5, DRAG / 16) → c_1
  37. Intersect(c_1, g, 1) → M
  38. Segment(B_3, C) → f_2
  39. Line(B, C) → g_2
  40. Point(g_2) → H_1
  41. Line(B, A) → h_2
  42. Circle(B_3, DRAG / 16) → e_1
  43. Point(e_1) → N
  44. Point(e_1) → O
  45. Point(h_2) → I_1
  46. Segment(B, H_1) → i_2
  47. Vector(B, H_1) → v
  48. Vector(B, I_1) → w
  49. Point(u) → P
  50. Circle(B_3, P) → f_1
  51. Circle(B_5, Segment[B_3, P]) → g_1
  52. Intersect(f_1, f_2, 1) → Q
  53. CircleArc(B_3, Q, P) → h_1
  54. Point(g_1) → R
  55. Point(u) → J_1
  56. CircleArc(B_5, R, J_1) → d_2
  57. Circle(J_1, Segment[P, Q]) → e_2
  58. Point(e_2) → K_1
  59. Point(e_2) → L_1
  60. CircleArc(J_1, K_1, L_1) → k_2
  61. Line(B_5, f_2) → j_2
  62. Intersect(i_2, j_2) → M_1
  63. Segment(B_5, M_1) → b_1
  64. Circle(C, Segment[P, Q]) → p_2
  65. Intersect(i_2, b_1) → C'
  66. Circle(M_1, Segment[P, Q]) → p_1
  67. Intersect(p_2, n_1, 1) → U
  68. Intersect(p_2, l_1, 1) → V
  69. CircleArc(C, U, V) → q_1
  70. Point(p_1) → W
  71. Intersect(p_1, i_2, 1) → Z
  72. CircleArc(M_1, W, Z) → r_1
  73. Circle(Z, Segment[U, V]) → s_1
  74. Point(s_1) → D_1
  75. Point(s_1) → N_1
  76. CircleArc(Z, D_1, N_1) → t_1
  77. Line(M_1, n_1) → l
  78. Point(w) → O_1
  79. Segment(B, O_1) → i_1
  80. Intersect(l, i_1) → A'_1
  81. Segment(B_5, M_1) → j_1
  82. Segment(M_1, A'_1) → a_1
  83. Intersect(i_1, a_1) → A'
  84. Polygon(A', B, C') → poly1, c', a', b
  85. Polygon(A, B, C) → poly2, c_2, a_2, b_2