对称轴 by Adam Bevan

对称轴 by Adam Bevan
几何画板及绘图内容加载中,请稍等……
2016-01-10 19:14
这个范例演示了图形的对称轴。核心数学概念包括几何中的对称性。使用了GeoGebra命令如Segment, Line, Mirror, Intersect等来构造图形。适合初中及以上学生学习几何对称性。

GeoGebra 命令及参数

  1. Segment(E, F) → p
  2. Line(J, K) → b_1
  3. Point(b_1) → L
  4. Point(b_1) → N
  5. Point(b_1) → O
  6. Point(b_1) → Q
  7. Mirror(M, b_1) → M'
  8. Point(b_1) → P
  9. Point(b_1) → R
  10. Segment(P, M) → c_1
  11. Segment(M, R) → f_1
  12. Segment(R, M') → g_1
  13. Segment(M', P) → h_1
  14. Segment(P, R) → i_1
  15. Segment(M, M') → j_1
  16. Intersect(i_1, j_1) → S
  17. Line(P, M') → k_1
  18. Line(M, R) → l_1
  19. Line(R, M') → m_1
  20. Line(M, P) → n_1
  21. Polygon(P, M, R, M') → poly3, p_1, m_2, r_1, m'
  22. Distance(P, M) → distancePM
  23. Distance(M, R) → distanceMR
  24. Distance(R, M') → distanceRM'
  25. Distance(M', P) → distanceM'P
  26. Angle(M', P, M) → ζ
  27. Angle(P, M, R) → η
  28. Angle(M, R, M') → θ
  29. Angle(R, M', P) → ι
  30. Angle(P, S, M') → κ
  31. Distance(M', M) → distanceM'M
  32. Distance(P, R) → distancePR
  33. Segment(T, U) → d_1
  34. Circle(S, Segment[U, T]) → e_1
  35. Point(e_1) → V
  36. Line(V, S) → q_1
  37. Mirror(P, q_1) → P'
  38. Mirror(M, q_1) → M'_1
  39. Mirror(R, q_1) → R'
  40. Mirror(M', q_1) → M''
  41. Polygon(P', M'_1, R', M'') → poly3', p', m'_1, r', m''
  42. Line(W, Z) → s_1
  43. Point(s_1) → B_1
  44. Point(s_1) → C_1
  45. Segment(B_1, C_1) → a_2
  46. Point(s_1) → D_1
  47. Point(s_1) → E_1
  48. Segment(D_1, E_1) → b_2
  49. Point(a_2) → H_1
  50. Line(A_1, F_1) → t_1
  51. Line(G_1, t_1) → c_2
  52. Point(c_2) → I_1
  53. Line(A_1, G_1) → h_2
  54. Line(F_1, I_1) → i_2
  55. Line(A_1, F_1) → j_2
  56. Line(I_1, G_1) → k_2
  57. Distance(G_1, A_1) → distanceG1A1
  58. Distance(A_1, F_1) → distanceA1F1
  59. Distance(F_1, I_1) → distanceF1I1
  60. Distance(I_1, G_1) → distanceI1G1
  61. Angle(I_1, G_1, A_1) → λ
  62. Angle(G_1, A_1, F_1) → μ
  63. Angle(A_1, F_1, I_1) → ν
  64. Angle(F_1, I_1, G_1) → ξ
  65. Segment(A_1, I_1) → l_2
  66. Segment(G_1, F_1) → n_2
  67. Intersect(l_2, n_2) → K_1
  68. Distance(G_1, F_1) → distanceG1F1
  69. Distance(A_1, I_1) → distanceA1I1
  70. Angle(G_1, K_1, I_1) → ο
  71. Polygon(G_1, A_1, F_1, I_1) → poly4, g_2, a_3, f_2, i_3
  72. Segment(J_1, L_1) → d_2
  73. Circle(K_1, Segment[J_1, L_1]) → e_2
  74. Point(e_2) → M_1
  75. Line(K_1, M_1) → p_2
  76. Mirror(G_1, p_2) → N_1
  77. Mirror(A_1, p_2) → O_1
  78. Mirror(F_1, p_2) → P_1
  79. Mirror(I_1, p_2) → Q_1
  80. Polygon(N_1, O_1, P_1, Q_1) → poly4', n_3, o_1, p_3, q_2
  81. Intersect(f_2, g_2) → Z_1
  82. Segment(B_2, C_2) → a_4
  83. Line(I_2, J_2) → d_4
  84. Line(K_2, d_4) → i_4
  85. Line(K_2, I_2) → j_4
  86. Line(J_2, j_4) → k_4
  87. Intersect(i_4, k_4) → L_2
  88. Polygon(K_2, I_2, J_2, L_2) → poly6, k_5, i_5, j_5, l_4
  89. Line(I_2, K_2) → m_4
  90. Line(J_2, L_2) → n_4
  91. Line(I_2, J_2) → p_4
  92. Line(K_2, L_2) → q_4
  93. Segment(K_2, J_2) → r_4
  94. Segment(I_2, L_2) → s_4
  95. Intersect(r_4, s_4) → M_2
  96. Segment(N_2, O_2) → t_4
  97. Circle(M_2, Segment[N_2, O_2]) → c_5
  98. Point(c_5) → P_2
  99. Line(M_2, P_2) → a_5
  100. Mirror(K_2, a_5) → Q_2
  101. Mirror(I_2, a_5) → R_2
  102. Mirror(J_2, a_5) → S_2
  103. Mirror(L_2, a_5) → T_2
  104. Polygon(Q_2, R_2, S_2, T_2) → poly6', q_5, r_5, s_5, t_5
  105. Distance(I_2, K_2) → distanceI2K2
  106. Distance(K_2, L_2) → distanceK2L2
  107. Distance(L_2, J_2) → distanceL2J2
  108. Distance(J_2, I_2) → distanceJ2I2
  109. Distance(I_2, L_2) → distanceI2L2
  110. Distance(K_2, J_2) → distanceK2J2
  111. Angle(J_2, I_2, K_2) → χ
  112. Angle(I_2, K_2, L_2) → ψ
  113. Angle(K_2, L_2, J_2) → ω
  114. Angle(L_2, J_2, I_2) → α_1
  115. Angle(I_2, M_2, J_2) → β_1
  116. Distance(I_2, J_2) → distanceI2J2
  117. Distance(I_2, L_2) → v_1
  118. Distance(K_2, J_2) → w_1
  119. Circle(U_2, V_2) → d_5
  120. Point(d_5) → W_2
  121. Segment(V_2, W_2) → b_5
  122. Mirror(U_2, b_5) → Z_2
  123. Polygon(W_2, U_2, V_2, Z_2) → poly7, w_2, u_2, v_2, z_2
  124. Segment(U_2, Z_2) → e_5
  125. Intersect(b_5, e_5) → A_3
  126. Distance(W_2, V_2) → distanceW2V2
  127. Distance(U_2, Z_2) → distanceU2Z2
  128. Angle(W_2, A_3, Z_2) → γ_1
  129. Angle(Z_2, W_2, U_2) → δ_1
  130. Angle(W_2, U_2, V_2) → ε_1
  131. Angle(U_2, V_2, Z_2) → ζ_1
  132. Angle(V_2, Z_2, W_2) → η_1
  133. Distance(W_2, U_2) → distanceW2U2
  134. Distance(U_2, V_2) → distanceU2V2
  135. Distance(V_2, Z_2) → distanceV2Z2
  136. Distance(Z_2, W_2) → distanceZ2W2
  137. Segment(B_3, C_3) → f_5
  138. Circle(A_3, Segment[B_3, C_3]) → g_5
  139. Point(g_5) → D_3
  140. Line(D_3, A_3) → h_5
  141. Mirror(W_2, h_5) → E_3
  142. Mirror(U_2, h_5) → F_3
  143. Mirror(V_2, h_5) → G_3
  144. Mirror(Z_2, h_5) → H_3
  145. Polygon(E_3, F_3, G_3, H_3) → poly7', e_6, f_6, g_6, h_6
  146. Line(W_2, U_2) → l_5
  147. Line(U_2, V_2) → m_5
  148. Line(V_2, Z_2) → n_5
  149. Line(Z_2, W_2) → p_5
  150. Segment(I_3, J_3) → a_6
  151. OrthogonalLine(I_3, a_6) → b_6
  152. OrthogonalLine(J_3, a_6) → c_6
  153. Point(b_6) → K_3
  154. Line(K_3, b_6) → d_6
  155. Line(K_3, d_6) → i_6
  156. Line(K_3, a_6) → j_6
  157. Intersect(c_6, j_6) → L_3
  158. Polygon(I_3, K_3, L_3, J_3) → poly8, i_7, k_6, l_6, j_7
  159. Distance(I_3, K_3) → distanceI3K3
  160. Distance(K_3, L_3) → distanceK3L3
  161. Distance(L_3, J_3) → distanceL3J3
  162. Distance(J_3, I_3) → distanceJ3I3
  163. Angle(J_3, I_3, K_3) → θ_1
  164. Angle(I_3, K_3, L_3) → ι_1
  165. Angle(K_3, L_3, J_3) → κ_1
  166. Angle(L_3, J_3, I_3) → λ_1
  167. Segment(K_3, J_3) → m_6
  168. Segment(I_3, L_3) → n_6
  169. Intersect(m_6, n_6) → M_3
  170. Line(I_3, K_3) → p_6
  171. Line(K_3, L_3) → q_6
  172. Line(L_3, J_3) → r_6
  173. Line(J_3, I_3) → s_6
  174. Angle(I_3, M_3, J_3) → μ_1
  175. Distance(I_3, L_3) → distanceI3L3
  176. Distance(K_3, J_3) → distanceK3J3
  177. Segment(N_3, O_3) → t_6
  178. Circle(M_3, Segment[N_3, O_3]) → c_7
  179. Point(c_7) → P_3
  180. Line(M_3, P_3) → a_7
  181. Mirror(I_3, a_7) → Q_3
  182. Mirror(K_3, a_7) → R_3
  183. Mirror(L_3, a_7) → S_3
  184. Mirror(J_3, a_7) → T_3
  185. Polygon(Q_3, R_3, S_3, T_3) → poly8', q_7, r_7, s_7, t_7
  186. Segment(A, G) → a
  187. OrthogonalLine(A, a) → b
  188. OrthogonalLine(G, a) → c
  189. Circle(A, Segment[A, G]) → d
  190. Circle(G, Segment[A, G]) → e
  191. Intersect(d, b, 2) → H
  192. Intersect(e, c, 2) → I
  193. Polygon(A, H, I, G) → poly1, a_1, h, i, g_7
  194. Segment(H, G) → l
  195. Segment(I, A) → n
  196. Intersect(l, n) → U_3
  197. Line(H, I) → q
  198. Line(G, A) → r
  199. Line(A, H) → b_7
  200. Line(I, G) → d_7
  201. Angle(G, U_3, I) → α
  202. Angle(G, A, H) → β
  203. Angle(A, H, I) → δ
  204. Angle(H, I, G) → ε
  205. Angle(I, G, A) → ν_1
  206. Distance(A, H) → distanceAH
  207. Distance(H, I) → distanceHI
  208. Distance(I, G) → distanceIG
  209. Distance(G, A) → distanceGA
  210. Distance(A, I) → distanceAI
  211. Distance(H, G) → distanceHG
  212. Segment(B_4, C_4) → m_7
  213. Segment(F_4, G_4) → a_8
  214. Circle(U_3, Segment[F_4, G_4]) → f_8
  215. Point(f_8) → H_4
  216. Line(U_3, H_4) → g_8
  217. Mirror(A, g_8) → A'
  218. Mirror(H, g_8) → H'
  219. Mirror(I, g_8) → I'
  220. Mirror(G, g_8) → G'
  221. Polygon(A', H', I', G') → poly1', a', h', i', g'
  222. Segment(B, C) → f

AI 绘图提示语参考

绘制一个几何图形,包含四边形PMRM'及其对称轴。首先画出线段PM,然后画出对称轴b1,接着画出点L、N、O、Q、P、R,利用镜像命令分别得到M'、P'、M'_1、R'、M'',最后画出四边形P'M'_1R'M''。
以上提示语为根据原始绘图命令整理而来,仅供参考。