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相似三角形 by Karen Krieger

相似三角形 by Karen Krieger
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2018-06-11 02:42
测试改名0角变换
这个范例演示了相似三角形的性质。它涉及相似三角形的核心概念，包括相似变换和角度对应关系。通过使用GeoGebra命令如Segment、LineBisector、Dilate等，可以构造出一系列相似三角形。适合初中和高中学生学习相似三角形的相关知识。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. LineBisector(a) → s_3
  3. Midpoint(a) → C_1
  4. Semicircle(A, B) → d
  5. Intersect(d, s_3, 1) → J_2
  6. CircleArc(C_1, B, J_2) → t_3
  7. Point(t_3) → C
  8. Segment(C, B) → f
  9. Segment(A, C) → e
  10. Min(a, f) → m
  11. Min(a, e) → l
  12. Min(l, m) → n
  13. OrthogonalLine(C_1, a) → b
  14. Circle(C_1, A) → c
  15. OrthogonalLine(C, a) → g
  16. Intersect(g, a) → E
  17. Segment(C, E) → h
  18. Angle(B, E, C) → α
  19. Angle(A, C, B) → β
  20. Polygon(A, E, C) → poly1, d_1, a_1, e_1
  21. Polygon(E, B, C) → poly2, d_2, e_2, b_1
  22. Circle(A, (0.2 * n)) → k
  23. Circle(C, (0.2 * n)) → p
  24. Circle(B, (0.2 * n)) → q
  25. Intersect(p, e_1, 1) → F
  26. Intersect(a_1, b_1) → G
  27. Intersect(a_1, b_1) → H
  28. Intersect(p, h, 1) → I
  29. Intersect(p, f, 1) → J
  30. Intersect(q, a, 1) → K
  31. Intersect(q, f, 1) → L
  32. Intersect(k, a, 1) → M
  33. Intersect(k, e, 1) → N
  34. CircleSector(A, M, N) → r
  35. Dilate(C, If[-2 < i < -1, -1 - i, 0], E) → D'
  36. Segment(C, D') → j
  37. CircleSector(B, L, K) → t
  38. Angle(C, E, A) → γ
  39. Dilate(A, If[-0.5 < i ≤ 0.5, 0.5 - i, 0], C) → A'
  40. Vector(A, A') → u
  41. Translate(r, u) → r'
  42. CircleArc(A, M, N) → f_1
  43. Dilate(B, If[1.5 < i ≤ 2.5, 2.5 - i, 0], C) → B'
  44. Vector(B, B') → v
  45. Translate(t, v) → t'
  46. CircleArc(B, L, K) → g_1
  47. Polygon(A, B, C) → poly3, d_3, a_2, b_2
  48. Rotate(r', If[0.5 < i ≤ 1.5, ((-(i - 0.5)) * π / 2), -1.5707963267948966], C) → r''
  49. Translate(t, v) → t'_1
  50. Rotate(t'_1, If[2.5 < i ≤ 3.5, (((i - 2.5) * 90))°, 90°], C) → s
  51. Mirror(E, f) → E'
  52. Mirror(E, e) → E'_1
  53. Dilate(E, If[4 < i ≤ 5, 5 - i, 0], E'_1) → E'_2
  54. Segment(C, E'_2) → h_1
  55. Segment(E'_2, A) → i_1
  56. Polygon(A, C, E'_2) → t1, e'_2, a_3, c_1
  57. Segment(A, C) → j_1
  58. Angle(A, E'_1, C) → δ
  59. Dilate(E, If[6 < i ≤ 7, 7 - i, 0], E') → E'_3
  60. Segment(C, E'_3) → k_1
  61. Segment(E'_3, B) → l_1
  62. Segment(C, B) → m_1
  63. Polygon(B, E'_3, C) → t2, c_2, b_3, e'_3
  64. Angle(C, E', B) → ε
  65. Angle(E, A, C) → ζ
  66. Centroid(t1) → D
  67. Centroid(t2) → O
  68. Centroid(poly3) → P
  69. Rotate(s, If[7 < i ≤ 8, ((-(i - 7)) * (π / 2 - ζ)), ζ - π / 2], C) → s'
  70. Rotate(r'', If[8 < i ≤ 9, ((i - 8) * ζ), ζ], C) → r'''
  71. Dilate(D, If[10 < i ≤ 11, 11 - i, 0], P) → D'_1
  72. Vector(D, D'_1) → w
  73. Translate(A, w) → A'_1
  74. Translate(C, w) → C'
  75. Translate(E'_2, w) → Q
  76. Polygon(A'_1, C', Q) → t1', q_1, a'_1, c'
  77. Translate(C, w) → C'_1
  78. Translate(E'_2, w) → R
  79. Segment(C'_1, R) → n_1
  80. Translate(E'_2, w) → S
  81. Translate(A, w) → A'_2
  82. Segment(S, A'_2) → p_1
  83. Translate(A, w) → A'_3
  84. Translate(C, w) → C'_2
  85. Segment(A'_3, C'_2) → r_1
  86. Translate(s', w) → s''
  87. Rotate(A'_1, If[10 < i ≤ 11, ((-(i - 10)) * ζ), (-ζ)], D'_1) → T
  88. Rotate(C', If[10 < i ≤ 11, ((-(i - 10)) * ζ), (-ζ)], D'_1) → C''
  89. Rotate(Q, If[10 < i ≤ 11, ((-(i - 10)) * ζ), (-ζ)], D'_1) → Q'
  90. Polygon(T, C'', Q') → t1'', q', t_1, c''
  91. Rotate(C'_1, If[10 < i ≤ 11, ((-(i - 10)) * ζ), (-ζ)], D'_1) → U
  92. Rotate(R, If[10 < i ≤ 11, ((-(i - 10)) * ζ), (-ζ)], D'_1) → R'
  93. Segment(U, R') → s_1
  94. Rotate(S, If[10 < i ≤ 11, ((-(i - 10)) * ζ), (-ζ)], D'_1) → S'
  95. Rotate(A'_2, If[10 < i ≤ 11, ((-(i - 10)) * ζ), (-ζ)], D'_1) → V
  96. Segment(S', V) → f_2
  97. Rotate(A'_3, If[10 < i ≤ 11, ((-(i - 10)) * ζ), (-ζ)], D'_1) → W
  98. Rotate(C'_2, If[10 < i ≤ 11, ((-(i - 10)) * ζ), (-ζ)], D'_1) → Z
  99. Segment(W, Z) → g_2
  100. Rotate(s'', If[10 < i ≤ 11, ((-(i - 10)) * ζ), (-ζ)], D'_1) → s'''
  101. Angle(T, S', U) → η
  102. Dilate(O, If[11 < i ≤ 12, 12 - i, 0], P) → O'
  103. Vector(O, O') → u_1
  104. Translate(B, u_1) → B'_1
  105. Translate(E'_3, u_1) → A_1
  106. Translate(C, u_1) → C'_3
  107. Polygon(B'_1, A_1, C'_3) → t2', c'_3, b'_1, a_4
  108. Translate(C, u_1) → C'_4
  109. Translate(E'_3, u_1) → D_1
  110. Segment(C'_4, D_1) → h_2
  111. Translate(E'_3, u_1) → E_1
  112. Translate(B, u_1) → B'_2
  113. Segment(E_1, B'_2) → i_2
  114. Translate(C, u_1) → C'_5
  115. Translate(B, u_1) → B'_3
  116. Segment(C'_5, B'_3) → j_2
  117. Translate(r''', u_1) → k_2
  118. Rotate(B'_1, If[11 < i ≤ 12, ((i - 11) * (π / 2 - ζ)), π / 2 - ζ], O') → B_1
  119. Rotate(A_1, If[11 < i ≤ 12, ((i - 11) * (π / 2 - ζ)), π / 2 - ζ], O') → F_1
  120. Rotate(C'_3, If[11 < i ≤ 12, ((i - 11) * (π / 2 - ζ)), π / 2 - ζ], O') → G_1
  121. Polygon(B_1, F_1, G_1) → t2'', g_3, b_4, f_3
  122. Rotate(C'_4, If[11 < i ≤ 12, ((i - 11) * (π / 2 - ζ)), π / 2 - ζ], O') → H_1
  123. Rotate(D_1, If[11 < i ≤ 12, ((i - 11) * (π / 2 - ζ)), π / 2 - ζ], O') → I_1
  124. Segment(H_1, I_1) → l_2
  125. Rotate(E_1, If[11 < i ≤ 12, ((i - 11) * (π / 2 - ζ)), π / 2 - ζ], O') → J_1
  126. Rotate(B'_2, If[11 < i ≤ 12, ((i - 11) * (π / 2 - ζ)), π / 2 - ζ], O') → K_1
  127. Segment(J_1, K_1) → m_2
  128. Rotate(C'_5, If[11 < i ≤ 12, ((i - 11) * (π / 2 - ζ)), π / 2 - ζ], O') → L_1
  129. Rotate(B'_3, If[11 < i ≤ 12, ((i - 11) * (π / 2 - ζ)), π / 2 - ζ], O') → M_1
  130. Segment(L_1, M_1) → n_2
  131. Rotate(k_2, If[11 < i ≤ 12, ((i - 11) * (π / 2 - ζ)), π / 2 - ζ], O') → p_2
  132. Angle(G_1, J_1, B_1) → θ
  133. Dilate(T, If[13 < i ≤ 14, 14 - i, 0], A) → T'
  134. Vector(T, T') → v_1
  135. Translate(T, v_1) → T'_1
  136. Translate(C'', v_1) → C'''
  137. Translate(Q', v_1) → Q''
  138. Polygon(T'_1, C''', Q'') → t1''', q'', t'_2, c'''
  139. Translate(S', v_1) → S''
  140. Translate(V, v_1) → V'
  141. Segment(S'', V') → q_2
  142. Translate(W, v_1) → W'
  143. Translate(Z, v_1) → Z'
  144. Segment(W', Z') → r_2
  145. Translate(U, v_1) → U'
  146. Translate(R', v_1) → R''
  147. Segment(U', R'') → s_2
  148. Translate(s''', v_1) → t_2
  149. Angle(Z', R'', V') → ι
  150. Dilate(G_1, If[13 < i ≤ 14, 14 - i, 0], A) → N_1
  151. Vector(G_1, N_1) → w_1
  152. Translate(B_1, w_1) → O_1
  153. Translate(F_1, w_1) → P_1
  154. Translate(G_1, w_1) → Q_1
  155. Polygon(O_1, P_1, Q_1) → t2''', q_3, o_1, p_3
  156. Translate(p_2, w_1) → c_3
  157. Translate(H_1, w_1) → R_1
  158. Translate(I_1, w_1) → S_1
  159. Segment(R_1, S_1) → h_3
  160. Translate(J_1, w_1) → T_1
  161. Translate(K_1, w_1) → U_1
  162. Segment(T_1, U_1) → i_3
  163. Translate(L_1, w_1) → V_1
  164. Translate(M_1, w_1) → W_1
  165. Segment(V_1, W_1) → j_3
  166. Angle(R_1, T_1, O_1) → κ
  167. Dilate(Z', If[15 < i ≤ 16, 16 - i, 0], B) → Z''
  168. Vector(Z', Z'') → u_2
  169. Translate(T'_1, u_2) → Z_1
  170. Translate(C''', u_2) → A_2
  171. Translate(Q'', u_2) → Q'''
  172. Polygon(Z_1, A_2, Q''') → t3, q''', z_1, a_5
  173. Translate(t_2, u_2) → e_3
  174. Translate(U', u_2) → U''
  175. Translate(R'', u_2) → R'''
  176. Segment(U'', R''') → k_3
  177. Translate(S'', u_2) → S'''
  178. Translate(V', u_2) → V''
  179. Segment(S''', V'') → l_3
  180. Angle(V'', S''', U'') → λ
  181. Dilate(O_1, If[15 < i ≤ 16, 16 - i, 0], B) → B_2
  182. Vector(O_1, B_2) → v_2
  183. Translate(O_1, v_2) → C_2
  184. Translate(P_1, v_2) → D_2
  185. Translate(Q_1, v_2) → E_2
  186. Polygon(C_2, D_2, E_2) → t4, e_4, c_4, d_4
  187. Translate(c_3, v_2) → r_3
  188. Translate(R_1, v_2) → F_2
  189. Translate(S_1, v_2) → G_2
  190. Segment(F_2, G_2) → m_3
  191. Translate(T_1, v_2) → H_2
  192. Translate(U_1, v_2) → I_2
  193. Segment(H_2, I_2) → n_3
  194. Angle(F_2, H_2, B_2) → μ

AI 绘图提示语参考

绘制两个相似三角形，三角形ABC和三角形EBC。首先，画出线段AB，然后作AB的中垂线，找到中点C，接着画以C为圆心的圆弧，连接点C和B，再连接点C和E，构造两个相似三角形，通过相似变换，分别以C为中心放大和缩小三角形ABC，得到三角形EBC和三角形ABC的相似三角形。
以上提示语为根据原始绘图命令整理而来，仅供参考。