相似图形:快速入门

相似图形:快速入门
几何画板及绘图内容加载中,请稍等……
2023-03-15 19:39
这个范例演示了相似图形的基本概念。它涉及相似三角形和比例关系。通过使用GeoGebra命令如Segment, Rotate, Ray, Point等,可以构造相似图形。适合初中和高中学生学习相似三角形和比例关系。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. Rotate(B, (a_{2} * pi / 180), A) → B'
  3. Ray(A, B') → f
  4. Point(f) → C
  5. Segment(A, C) → b
  6. OrthogonalLine(C, b) → r
  7. Circle(C, 1) → t
  8. Intersect(t, r, 2) → K
  9. OrthogonalLine(K, r) → i_1
  10. Point(i_1) → W
  11. Rotate(E, (a_{2} * pi / 180), D) → E'
  12. Ray(D, E') → j
  13. Segment(D, E) → a'
  14. Circle(D, (a' / a * b)) → d
  15. Intersect(d, j, 1) → F
  16. Segment(D, F) → b'
  17. Line(K, b') → k_1
  18. Point(k_1) → U
  19. Line(K, a') → j_1
  20. Point(j_1) → V
  21. Circle(B, 1) → s
  22. OrthogonalLine(B, a) → q
  23. Point(q) → M
  24. Intersect(s, q, 1) → J
  25. OrthogonalLine(J, q) → h_1
  26. Point(h_1) → P
  27. Polygon(A, B, C) → t1, c_{2}, a_1, b_{1}
  28. Polygon(D, F, E) → t2, e, d_1, f_1
  29. Min({a, a', b, b'}) → g
  30. Circle(A, (0.35 * g)) → h
  31. Intersect(h, a, 1) → G
  32. Intersect(h, b, 1) → H
  33. CircleSector(A, G, H) → k
  34. Line(A, a') → i
  35. Dilate(A, If[6 < l ≤ 7, 7 - l, 0], D) → A'
  36. Vector(A, A') → u
  37. Translate(k, u) → k'
  38. Point(i) → I
  39. Angle(I, A, B) → α
  40. CircleArc(A, G, H) → p
  41. Dilate(D, If[1 < l ≤ 2, 2 - l, 0], J) → D'
  42. Vector(D, D') → v
  43. Translate(D, v) → D'_{1}
  44. Translate(E, v) → E'_{1}
  45. Segment(D'_{1}, E'_{1}) → a''
  46. Line(J, a') → g_1
  47. Point(g_1) → L
  48. Angle(P, J, L) → β
  49. Rotate(D'_{1}, If[1 < l ≤ 2, ((l - 1) * β), β], D'_{1}) → N
  50. Rotate(E'_{1}, If[1 < l ≤ 2, ((-(l - 1)) * β), (-β)], D'_{1}) → O
  51. Segment(N, O) → a'''
  52. Dilate(D, If[2 < l ≤ 3, 3 - l, 0], K) → D'_{2}
  53. Vector(D, D'_{2}) → w
  54. Translate(D, w) → D'_{3}
  55. Translate(E, w) → E'_{2}
  56. Point(j_1) → Q
  57. Point(i_1) → R
  58. Angle(W, K, U) → γ
  59. Rotate(D'_{3}, If[2 < l ≤ 3, ((l - 2) * γ), γ], D'_{3}) → S
  60. Rotate(E'_{2}, If[2 < l ≤ 3, ((l - 2) * γ), γ], D'_{3}) → T
  61. Translate(D, w) → D'_{4}
  62. Translate(F, w) → F'
  63. Segment(D'_{4}, F') → b''
  64. Rotate(D'_{4}, If[2 < l ≤ 3, ((-(l - 2)) * γ), (-γ)], K) → Z
  65. Rotate(F', If[2 < l ≤ 3, ((-(l - 2)) * γ), (-γ)], K) → F''
  66. Segment(Z, F'') → b'''
  67. If(o, 7, 4) → c_1
  68. Angle(A, C, B) → δ
  69. Intersect(t, b, 1) → A_1
  70. Rotate(A_1, If[4 < l ≤ 5, ((l - 4) * δ), δ], C) → B_1
  71. CircleSector(C, A_1, B_1) → e_1
  72. Dilate(C, If[6 < l ≤ 7, 7 - l, 0], F) → C'
  73. Vector(C, C') → u_1
  74. Translate(e_1, u_1) → p_1
  75. Line(C, b') → l_1
  76. Point(l_1) → C_1
  77. Angle(C_1, C, A) → ε
  78. Segment(F, E) → m_1
  79. Segment(B, C) → c
  80. OrthogonalLine(B, c) → r_1
  81. Circle(B, 1) → s_1
  82. Intersect(s_1, r_1, 1) → D_1
  83. Dilate(E, If[3 < l ≤ 4, 4 - l, 0], D_1) → E'_{3}
  84. Vector(E, E'_{3}) → v_1
  85. Translate(F, v_1) → F'_{1}
  86. Translate(E, v_1) → E'_{4}
  87. Segment(F'_{1}, E'_{4}) → t_1
  88. Line(E, c) → f_2
  89. Point(f_2) → E_1
  90. Angle(F, E, E_1) → ζ
  91. Rotate(F'_{1}, If[3 < l ≤ 4, ((l - 3) * ζ), ζ], E'_{3}) → F_1
  92. Rotate(E'_{4}, If[3 < l ≤ 4, ((l - 3) * ζ), ζ], E'_{3}) → G_1
  93. Segment(F_1, G_1) → g_2
  94. Rotate(p_1, If[6 < l ≤ 7, ((-(l - 6)) * ε), (-ε)], C') → q_1
  95. Angle(B, A, C) → η
  96. Rotate(G, If[4 < l ≤ 5, ((l - 4) * η), η], A) → G'
  97. CircleSector(A, G, G') → d_2
  98. CircleArc(C, A_1, B_1) → e_2
  99. Rotate(k', If[6 < l ≤ 7, ((-(l - 6)) * α), (-α)], A') → k''
  100. Circle(B, (0.35 * g)) → h_2
  101. Intersect(h_2, c, 1) → H_1
  102. Intersect(h_2, a, 1) → I_1
  103. Angle(C, B, A) → θ
  104. Rotate(H_1, If[4 < l ≤ 5, ((l - 4) * θ), θ], B) → J_1
  105. CircleSector(B, H_1, J_1) → k_2
  106. Line(B, m_1) → n_1
  107. Point(n_1) → K_1
  108. Angle(K_1, B, C) → λ
  109. Dilate(B, If[6 < l ≤ 7, 7 - l, 0], E) → B'_{1}
  110. Vector(B, B'_{1}) → w_1
  111. Translate(k_2, w_1) → p_2
  112. Rotate(p_2, If[6 < l ≤ 7, ((-(l - 6)) * λ), (-λ)], B'_{1}) → q_2
  113. CircleArc(B, H_1, I_1) → r_2

AI 绘图提示语参考

请绘制一个包含相似三角形的图形。首先,构造点A和B,然后旋转点B得到B'。接着,构造射线从A到B',并找到射线上的点C。然后,构造线段AC和过C的垂直线,以及以C为圆心半径为1的圆。圆与垂直线的交点为K,过K的垂直线与垂直线交于W。继续构造点D、E、F等,形成另一个三角形。构造相似比和圆弧,最终得到两个相似图形。确保图形中包含旋转、射线、圆和相似关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。