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Oscar的平行四边形、菱形、矩形、正方形、筝形、梯形

Oscar的平行四边形、菱形、矩形、正方形、筝形、梯形
几何画板及绘图内容加载中，请稍等……
2016-03-17 22:43
多边形角几何作图
这个范例展示了Oscar的平行四边形、菱形、矩形、正方形、筝形和梯形。它涉及的核心数学概念包括几何作图、角度、距离和构造。通过使用GeoGebra命令如Line、Point、Segment、Intersect、Angle、Circle等，可以构建这些图形。适合初中和高中学生学习几何作图和相关概念。

GeoGebra 命令及参数

  1. Line(A, B) → a
  2. Line(C, a) → b
  3. Point(b) → D
  4. Segment(A, D) → c
  5. Line(B, c) → d
  6. Intersect(d, b) → E
  7. Segment(B, E) → e
  8. Segment(A, B) → f
  9. Segment(E, D) → g
  10. Angle(A, B, E) → α
  11. Angle(B, E, D) → β
  12. Angle(E, D, A) → γ
  13. Angle(D, A, B) → δ
  14. Segment(B, D) → h
  15. Segment(A, E) → i
  16. Intersect(i, h) → F
  17. Angle(A, F, D) → ε
  18. Angle(D, F, E) → ζ
  19. Angle(E, F, B) → η
  20. Angle(B, F, A) → θ
  21. Circle(G, H) → k
  22. Point(k) → I
  23. Circle(I, G) → p
  24. Circle(H, G) → q
  25. Intersect(p, q, 2) → J
  26. Segment(I, J) → j
  27. Segment(J, H) → l
  28. Segment(H, G) → m
  29. Segment(G, I) → n
  30. Segment(J, G) → r
  31. Segment(I, H) → s
  32. Intersect(r, s) → K
  33. Segment(I, K) → t
  34. Segment(K, H) → a_1
  35. Segment(J, K) → b_1
  36. Segment(K, G) → c_1
  37. Angle(H, K, J) → ι
  38. Angle(G, K, H) → κ
  39. Angle(I, K, G) → λ
  40. Angle(J, K, I) → μ
  41. Segment(L, M) → d_1
  42. Line(N, d_1) → e_1
  43. OrthogonalLine(L, e_1) → f_1
  44. Intersect(f_1, e_1) → O
  45. OrthogonalLine(M, e_1) → g_1
  46. Intersect(e_1, g_1) → P
  47. Segment(L, O) → h_1
  48. Segment(O, P) → i_1
  49. Segment(P, M) → j_1
  50. Angle(O, L, M) → ν
  51. Angle(L, M, P) → ξ
  52. Angle(M, P, O) → ο
  53. Angle(P, O, L) → ρ
  54. Segment(M, O) → k_1
  55. Segment(L, P) → l_1
  56. Intersect(l_1, k_1) → Q
  57. Segment(M, Q) → m_1
  58. Segment(Q, L) → n_1
  59. Segment(Q, O) → p_1
  60. Segment(Q, P) → q_1
  61. Angle(L, Q, O) → σ
  62. Angle(O, Q, P) → τ
  63. Angle(P, Q, M) → υ
  64. Angle(M, Q, L) → ϕ
  65. Segment(R, S) → r_1
  66. OrthogonalLine(R, r_1) → s_1
  67. OrthogonalLine(S, r_1) → t_1
  68. Circle(R, S) → c_2
  69. Intersect(c_2, s_1, 2) → T
  70. OrthogonalLine(T, s_1) → a_2
  71. Intersect(t_1, a_2) → U
  72. Segment(R, T) → b_2
  73. Segment(T, U) → d_2
  74. Segment(U, S) → e_2
  75. Angle(R, T, U) → χ
  76. Angle(T, U, S) → ψ
  77. Angle(U, S, R) → ω
  78. Angle(S, R, T) → α_1
  79. Segment(V, W) → f_2
  80. Point(f_2) → Z
  81. OrthogonalLine(Z, f_2) → g_2
  82. Point(g_2) → A_1
  83. Circle(Z, A_1) → h_2
  84. Intersect(h_2, g_2, 2) → B_1
  85. Point(h_2) → C_1
  86. Segment(V, A_1) → i_2
  87. Segment(V, B_1) → j_2
  88. Segment(B_1, W) → k_2
  89. Segment(W, A_1) → l_2
  90. Segment(D_1, E_1) → m_2
  91. Point(m_2) → F_1
  92. OrthogonalLine(F_1, m_2) → n_2
  93. Point(n_2) → G_1
  94. Circle(F_1, G_1) → p_2
  95. Intersect(p_2, n_2, 2) → H_1
  96. Segment(D_1, G_1) → q_2
  97. Segment(D_1, H_1) → r_2
  98. Segment(H_1, E_1) → s_2
  99. Segment(E_1, G_1) → t_2
  100. Segment(I_1, J_1) → a_3
  101. OrthogonalLine(I_1, a_3) → b_3
  102. OrthogonalLine(J_1, a_3) → c_3
  103. Point(b_3) → K_1
  104. OrthogonalLine(K_1, b_3) → d_3
  105. Intersect(c_3, d_3) → L_1
  106. Segment(K_1, L_1) → e_3
  107. Point(e_3) → M_1
  108. Segment(I_1, M_1) → f_3
  109. Circle(J_1, f) → g_3
  110. Intersect(g_3, e_3, 1) → N_1
  111. Segment(J_1, N_1) → h_3
  112. Segment(M_1, N_1) → i_3
  113. Segment(O_1, P_1) → j_3
  114. OrthogonalLine(O_1, j_3) → k_3
  115. OrthogonalLine(P_1, j_3) → l_3
  116. Point(k_3) → Q_1
  117. OrthogonalLine(Q_1, k_3) → m_3
  118. Intersect(l_3, m_3) → R_1
  119. Segment(Q_1, R_1) → n_3
  120. Point(n_3) → S_1
  121. Segment(O_1, S_1) → p_3
  122. Circle(P_1, 3.08) → q_3
  123. Circle(P_1, 3.124410319967215) → r_3
  124. Point(r_3) → T_1
  125. Circle(P_1, 6.95) → s_3
  126. Circle(P_1, 6.919440774045372) → t_3
  127. Point(s_3) → U_1
  128. Circle(P_1, 6.962364924165079) → c_4
  129. Point(Circle[V_1, 9]) → W_1
  130. Segment(V_1, W_1) → a_4
  131. Line(Z_1, a_4) → b_4
  132. Point(b_4) → A_2
  133. Segment(V_1, A_2) → d_4
  134. Circle(W_1, 6.83) → e_4
  135. Intersect(e_4, b_4, 1) → B_2
  136. Segment(W_1, B_2) → f_4
  137. Segment(A_2, B_2) → g_4
  138. Segment(C_2, D_2) → h_4
  139. OrthogonalLine(C_2, h_4) → i_4
  140. OrthogonalLine(D_2, h_4) → j_4
  141. Point(i_4) → E_2
  142. OrthogonalLine(E_2, i_4) → k_4
  143. Intersect(j_4, k_4) → F_2
  144. Segment(E_2, F_2) → l_4
  145. Point(l_4) → G_2
  146. Point(l_4) → H_2
  147. Point(l_4) → J_2
  148. Segment(G_2, J_2) → m_4
  149. Segment(C_2, G_2) → n_4
  150. Segment(D_2, J_2) → p_4
  151. Segment(D_1, E_1) → q_4
  152. Segment(G_1, H_1) → r_4
  153. Segment(D_1, F_1) → s_4
  154. Segment(F_1, E_1) → t_4
  155. Segment(G_1, F_1) → a_5
  156. Segment(F_1, H_1) → b_5
  157. Angle(G_1, F_1, E_1) → β_1
  158. Angle(E_1, F_1, G_1) → γ_1
  159. Angle(H_1, F_1, E_1) → δ_1
  160. Angle(D_1, F_1, H_1) → ε_1
  161. Angle(G_1, F_1, D_1) → ζ_1
  162. Distance(q_2, t_2) → o
  163. Distance(U, d_2) → distanceUd2
  164. Segment(K_2, L_2) → c_5
  165. OrthogonalLine(M_2, c_5) → d_5
  166. OrthogonalLine(K_2, c_5) → e_5
  167. OrthogonalLine(L_2, c_5) → f_5
  168. Point(e_5) → N_2
  169. OrthogonalLine(O_2, e_5) → g_5
  170. OrthogonalLine(N_2, e_5) → h_5
  171. Intersect(f_5, h_5) → P_2
  172. Segment(N_2, P_2) → i_5
  173. Point(i_5) → Q_2
  174. Point(i_5) → R_2
  175. Point(i_5) → S_2
  176. Segment(Q_2, K_2) → j_5
  177. Segment(Q_2, R_2) → k_5
  178. Segment(R_2, L_2) → l_5
  179. Angle(K_2, Q_2, R_2) → η_1
  180. Angle(Q_2, R_2, L_2) → θ_1
  181. Angle(R_2, L_2, K_2) → ι_1
  182. Angle(L_2, K_2, Q_2) → κ_1
  183. Segment(T_2, U_2) → m_5
  184. OrthogonalLine(T_2, m_5) → n_5
  185. OrthogonalLine(U_2, m_5) → p_5
  186. Point(n_5) → V_2
  187. OrthogonalLine(V_2, p_5) → q_5
  188. Intersect(p_5, q_5) → W_2
  189. Segment(R_2, Z_2) → r_5
  190. Point(r_5) → A_3
  191. Segment(A_3, B_3) → s_5
  192. Segment(V_2, W_2) → t_5
  193. Point(t_5) → D_3
  194. Segment(D_3, T_2) → a_6
  195. Circle(U_2, 3.07) → c_6
  196. Intersect(c_6, t_5, 1) → E_3
  197. Segment(E_3, U_2) → b_6
  198. Segment(D_3, E_3) → d_6
  199. Circle(U_2, 3.07) → e_6
  200. Segment(E_3, U_2) → f_6
  201. Segment(F_3, G_3) → g_6
  202. OrthogonalLine(F_3, g_6) → h_6
  203. OrthogonalLine(G_3, g_6) → i_6
  204. Point(h_6) → H_3
  205. OrthogonalLine(H_3, h_6) → j_6
  206. Intersect(i_6, j_6) → I_3
  207. Segment(H_3, I_3) → k_6
  208. Point(k_6) → J_3
  209. Segment(F_3, J_3) → l_6
  210. Circle(G_3, 3.76) → p_6
  211. Intersect(p_6, k_6, 1) → K_3
  212. Segment(G_3, K_3) → m_6
  213. Segment(J_3, K_3) → n_6
  214. Angle(F_3, J_3, K_3) → λ_1
  215. Angle(J_3, K_3, G_3) → μ_1
  216. Angle(K_3, G_3, F_3) → ν_1
  217. Angle(G_3, F_3, J_3) → ξ_1
  218. Point(Circle[L_3, 9]) → M_3
  219. Segment(L_3, M_3) → q_6
  220. Line(N_3, q_6) → r_6
  221. Point(r_6) → O_3
  222. Segment(L_3, O_3) → s_6
  223. Circle(M_3, 6.83) → t_6
  224. Intersect(t_6, r_6, 1) → P_3
  225. Segment(M_3, P_3) → a_7
  226. Segment(O_3, P_3) → b_7
  227. Segment(Q_3, R_3) → c_7
  228. OrthogonalLine(Q_3, c_7) → d_7
  229. OrthogonalLine(R_3, c_7) → e_7
  230. Point(d_7) → S_3
  231. OrthogonalLine(S_3, d_7) → f_7
  232. Intersect(e_7, f_7) → T_3
  233. Segment(S_3, T_3) → g_7
  234. Point(g_7) → U_3
  235. Segment(Q_3, U_3) → h_7
  236. Circle(R_3, 3.75) → k_7
  237. Intersect(k_7, g_7, 1) → V_3
  238. Segment(R_3, V_3) → i_7
  239. Segment(U_3, V_3) → j_7
  240. Angle(Q_3, U_3, V_3) → ο_1
  241. Angle(U_3, V_3, R_3) → ρ_1
  242. Angle(V_3, R_3, Q_3) → σ_1
  243. Angle(R_3, Q_3, U_3) → τ_1

AI 绘图提示语参考

绘制一个平行四边形，然后在其基础上构造一个菱形、矩形、正方形、筝形和梯形。首先画出两条相交的直线AB和BC，接着过点B作直线AB的平行线，交直线BC于点D，连接AD和BD，得到平行四边形ABCD。接着以点D为圆心，DA为半径画圆，交直线AB于点E，连接BE，得到菱形ABED。再以点E为圆心，EA为半径画圆，交直线BD于点F，连接EF，得到矩形ABEF。然后以点F为圆心，FA为半径画圆，交直线BE于点G，连接FG，得到正方形ABFG。接着以点G为圆心，GA为半径画圆，交直线EF于点H，连接GH，得到筝形ABGH。最后以点H为圆心，HA为半径画圆，交直线FG于点I，连接HI，得到梯形ABHI。
以上提示语为根据原始绘图命令整理而来，仅供参考。