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Basic Shapes

Basic Shapes
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2020-04-30 16:44
VectorCoordinate GeometryGeometric Construction
This example demonstrates the construction and transformation of fundamental geometric shapes. Key math concepts include geometric construction, transformation, vectors, and coordinate geometry. It utilizes commands and objects such as Rotate, Ray, Intersect, Segment, Mirror, Point, Polygon, Midpoint, Vector, Line, CircleArc, Circle, Plane, Distance, OrthogonalLine, and Sequence. Suitable for middle school students and above to develop geometric drawing skills and spatial reasoning.

GeoGebra Commands & Parameters

  1. Rotate(B_1, 45°, A_1) → C_1
  2. Rotate(C_1, (-(22.5°)), A_1) → J_1
  3. Ray(A_1, J_1) → l_2
  4. Intersect(vgl1, l_2) → N_1
  5. Segment(V, U) → g_2
  6. Rotate(V, 22.5°, Z) → V'
  7. Ray(Z, V') → f_2
  8. Mirror(V, f_2) → V'_1
  9. Intersect(g_2, f_2) → I_1
  10. Point(yAxis) → A
  11. Polygon(A, B, 4) → veelhoek1, f, g, h, i, C, D
  12. Point(yAxis) → E
  13. Rotate(F, (-(67.5°)), E) → F'
  14. Point(yAxis) → H
  15. Rotate(H, (-(22.5°)), G) → H'
  16. Ray(G, H') → j
  17. Ray(E, F') → k
  18. Intersect(j, k) → I
  19. Polygon(E, I, G, F) → vierhoek1, e, i_1, g_1, f_1
  20. Point(yAxis) → K
  21. Point(yAxis) → L
  22. Rotate(L, (-(22.5°)), M) → L'
  23. Rotate(L, 22.5°, K) → L'_1
  24. Ray(K, L'_1) → l
  25. Ray(M, L') → m
  26. Intersect(l, m) → N
  27. Polygon(K, L, M, N) → vierhoek2, k_1, l_1, m_1, n
  28. Point(yAxis) → O
  29. Intersect(xAxis, yAxis) → P
  30. Point(xAxis) → Q
  31. Polygon((1, 0), (1, 1), (0, 1)) → driehoek1, p, q, b_9
  32. Rotate(S, 45°, R) → S'
  33. Polygon(R, S, T, S') → vierhoek3, r, s, t, s'
  34. Midpoint(V, U) → W
  35. Rotate(W, (-(90°)), U) → W'
  36. Polygon(Z, V, I_1, V'_1) → vierhoek4, h_2, i_2, j_2, k_2
  37. Midpoint(D_1, C_1) → E_1
  38. Polygon(A_1, B_1, N_1, C_1) → vierhoek5, a_1, b_1, c_1, e_1
  39. Point(xAxis) → F_1
  40. Point(xAxis) → G_1
  41. Rotate(G_1, 45°, F_1) → H_1
  42. Polygon(F_1, G_1, H_1) → driehoek2, h_1, a, b
  43. Vector(A, D) → u
  44. Vector(A, B) → d
  45. Vector(D, C) → u_1
  46. Vector(B, C) → v_1
  47. Vector(I, E) → w_1
  48. Vector(I, G) → d_1
  49. Vector(E, F) → j_1
  50. Vector(G, F) → n_1
  51. Vector(L, K) → p_1
  52. Vector(L, M) → q_1
  53. Vector(M, N) → r_1
  54. Vector(K, N) → s_1
  55. Segment(O, Q) → t_1
  56. Vector(R, S') → w_2
  57. Vector(R, S) → a_2
  58. Vector(S, T) → b_2
  59. Vector(S', T) → c_2
  60. Vector(I_1, V) → v
  61. Vector(I_1, V'_1) → w
  62. Vector(V, Z) → d_2
  63. Vector(V'_1, Z) → e_2
  64. Line(K_1, L_1) → m_2
  65. Intersect(m_2, l_2) → M_1
  66. Line(A_1, B_1) → n_2
  67. Vector(A_1, C_1) → p_2
  68. Vector(A_1, B_1) → q_2
  69. Segment(C_1, N_1) → r_2
  70. Segment(N_1, B_1) → s_2
  71. Segment(H_1, G_1) → t_2
  72. Vector(H_1, F_1) → u_3
  73. Vector(G_1, F_1) → v_3
  74. Intersect(yAxis, xAxis) → O_1
  75. Point(xAxis) → P_1
  76. Point(zAxis) → Q_1
  77. Segment(O_1, Q_1) → verthoek00
  78. Segment(P_1, R_1) → verthoek0
  79. Segment(Q_1, R_1) → f_3
  80. CircleArc(U_1, W_1, T_1) → boog0
  81. Segment(S_1, T_1) → vertmidden0
  82. Segment(W_1, V_1) → vertklein0
  83. Segment(P_1, S_1) → onder0
  84. Segment(R_1, V_1) → boven0
  85. Line(U_1, V_1) → as
  86. Rotate(P_1, (-(90°)), as) → Z_1
  87. Rotate(S_1, (-(90°)), as) → A_2
  88. Segment(Z_1, A_2) → onder0'
  89. Rotate(R_1, (-(90°)), as) → B_2
  90. Rotate(V_1, (-(90°)), as) → C_2
  91. Segment(B_2, C_2) → boven0'
  92. Rotate(boog0, (-(90°)), as) → boog0'
  93. Rotate(S_1, (-(90°)), as) → D_2
  94. Rotate(T_1, (-(90°)), as) → E_2
  95. Segment(D_2, E_2) → vertmidden0'
  96. Segment(Q_1, B_2) → g_3
  97. Intersect(as, xOyPlane) → F_2
  98. Rotate(P_1, (-(90°)), as) → G_2
  99. Rotate(R_1, (-(90°)), as) → H_2
  100. Segment(G_2, H_2) → verthoek0'
  101. Polygon(P_1, F_2, Z_1, O_1) → vierhoek6, h_3, i_3, z_1, o_1
  102. Segment(K_2, P_1) → j_3
  103. Segment(Z_1, L_2) → k_3
  104. Segment(O_1, J_2) → l_3
  105. Segment(J_2, K_2) → m_3
  106. Segment(J_2, L_2) → n_3
  107. Segment(I_2, P_1) → p_3
  108. Segment(I_2, Z_1) → q_3
  109. Circle(P_1, 0.2, j_3) → c_3
  110. Plane(O_1, F_2, J_2) → diag
  111. Segment(K_2, M_2) → r_3
  112. Segment(M_2, L_2) → s_3
  113. Segment(M_2, I_2) → t_3
  114. CircleArc(P_2, Q_2, O_2) → d_3
  115. Segment(K_2, R_2) → a_3
  116. Segment(R_2, Q_2) → b_3
  117. Segment(O_2, N_2) → e_3
  118. Segment(P_1, N_2) → f_4
  119. Mirror(K_2, diag) → S_2
  120. Mirror(R_2, diag) → T_2
  121. Segment(S_2, T_2) → g_4
  122. Mirror(d_3, diag) → c_4
  123. Mirror(O_2, diag) → U_2
  124. Mirror(N_2, diag) → V_2
  125. Segment(U_2, V_2) → h_4
  126. Mirror(P_1, diag) → W_2
  127. Mirror(N_2, diag) → Z_2
  128. Segment(W_2, Z_2) → i_4
  129. Segment(C_3, P_1) → j_4
  130. Segment(A_3, O_1) → k_4
  131. Circle(P_1, 0.2, j_4) → d_4
  132. Segment(I_2, P_1) → l_4
  133. Intersect(l_4, d_4) → D_3, E_3
  134. Segment(Z_1, I_2) → m_4
  135. Distance(E_3, I_2) → o_2
  136. Distance(I_2, P_1) → o_3
  137. CircleArc(J_3, H_3, I_3) → e_4
  138. Segment(I_3, E_3) → n_4
  139. Segment(P_1, E_3) → p_4
  140. Segment(C_3, K_3) → q_4
  141. Segment(K_3, H_3) → r_4
  142. Segment(O_1, P_1) → s_4
  143. Mirror(C_3, diag) → M_3
  144. Mirror(K_3, diag) → N_3
  145. Segment(M_3, N_3) → t_4
  146. Mirror(e_4, diag) → c_5
  147. Mirror(I_3, diag) → O_3
  148. Mirror(E_3, diag) → P_3
  149. Segment(O_3, P_3) → a_4
  150. Mirror(C_3, diag) → Q_3
  151. Mirror(P_1, diag) → R_3
  152. Segment(Q_3, R_3) → b_4
  153. Mirror(P_1, diag) → S_3
  154. Mirror(E_3, diag) → T_3
  155. Segment(S_3, T_3) → f_5
  156. Mirror(O_1, diag) → U_3
  157. Mirror(P_1, diag) → V_3
  158. Segment(U_3, V_3) → g_5
  159. Segment(A_3, C_3) → h_5
  160. Mirror(A_3, diag) → W_3
  161. Mirror(C_3, diag) → Z_3
  162. Segment(W_3, Z_3) → i_5
  163. Segment(C_4, A_4) → k_5
  164. Segment(B_4, A_4) → q_5
  165. Mirror(D_4, diag) → H_4
  166. Mirror(O_1, diag) → I_4
  167. Mirror(E_4, diag) → J_4
  168. Mirror(D_4, diag) → K_4
  169. Segment(J_4, K_4) → s_5
  170. Mirror(C_4, diag) → L_4
  171. Mirror(A_4, diag) → M_4
  172. Segment(L_4, M_4) → t_5
  173. Mirror(A_4, diag) → N_4
  174. Mirror(G_4, diag) → O_4
  175. Segment(R_4, P_1) → j_5
  176. Segment(S_4, O_1) → f_6
  177. Polygon(O_1, P_1, T_4, P_4) → vierhoek7, g_6, h_6, i_6, j_6
  178. Circle(P_1, 0.2, j_5) → c_6
  179. Intersect(h_6, c_6) → U_4,
  180. CircleArc(W_4, Z_4, V_4) → d_6
  181. Segment(V_4, U_4) → k_6
  182. Segment(R_4, A_5) → l_6
  183. Segment(A_5, Z_4) → m_6
  184. Segment(U_4, P_1) → n_6
  185. Plane(O_1, T_4, S_4) → diag1
  186. Mirror(U_4, diag1) → B_5
  187. Mirror(P_1, diag1) → C_5
  188. Segment(B_5, C_5) → p_6
  189. Mirror(R_4, diag1) → D_5
  190. Mirror(P_1, diag1) → E_5
  191. Segment(D_5, E_5) → q_6
  192. Mirror(V_4, diag1) → F_5
  193. Mirror(U_4, diag1) → G_5
  194. Segment(F_5, G_5) → r_6
  195. Mirror(d_6, diag1) → e_6
  196. Mirror(R_4, diag1) → H_5
  197. Mirror(A_5, diag1) → I_5
  198. Segment(H_5, I_5) → s_6
  199. Segment(S_4, R_4) → t_6
  200. Segment(S_4, H_5) → a_6
  201. Segment(L_5, J_5) → b_6
  202. OrthogonalLine(L_5, b_6, xOyPlane) → f_7
  203. Intersect(f_7, yAxis) → M_5
  204. Segment(K_5, M_5) → g_7
  205. Segment(M_5, L_5) → h_7
  206. Segment(K_5, J_5) → i_7
  207. Segment(O_5, L_5) → j_7
  208. Segment(O_5, P_5) → k_7
  209. Segment(N_5, O_5) → l_7
  210. Segment(N_5, M_5) → m_7
  211. Circle(L_5, 0.2, j_7) → c_7
  212. Intersect(b_6, c_7) → Q_5,
  213. CircleArc(S_5, T_5, R_5) → d_7
  214. Segment(P_5, T_5) → n_7
  215. Segment(R_5, Q_5) → p_7
  216. Segment(L_5, Q_5) → q_7
  217. Plane(M_5, J_5, N_5) → diag2
  218. Mirror(R_5, diag2) → U_5
  219. Mirror(Q_5, diag2) → V_5
  220. Segment(U_5, V_5) → r_7
  221. Mirror(P_5, diag2) → W_5
  222. Mirror(T_5, diag2) → Z_5
  223. Segment(W_5, Z_5) → s_7
  224. Mirror(L_5, diag2) → A_6
  225. Mirror(Q_5, diag2) → B_6
  226. Segment(A_6, B_6) → t_7
  227. Mirror(d_7, diag2) → e_7
  228. Mirror(O_5, diag2) → C_6
  229. Mirror(L_5, diag2) → D_6
  230. Segment(C_6, D_6) → a_7
  231. Mirror(N_5, diag2) → E_6
  232. Mirror(O_5, diag2) → F_6
  233. Segment(E_6, F_6) → b_7
  234. Mirror(O_5, diag2) → G_6
  235. Mirror(P_5, diag2) → H_6
  236. Segment(G_6, H_6) → f_8
  237. Rotate(P_1, 45°, zAxis) → I_6
  238. Segment(J_6, P_1) → g_8
  239. Segment(I_6, J_6) → h_8
  240. Segment(I_6, O_1) → i_8
  241. Segment(O_1, P_1) → j_8
  242. Segment(M_6, P_1) → l_8
  243. Segment(K_6, Q_6) → n_8
  244. Segment(Q_6, L_6) → p_8
  245. Mirror(Q_6, diag1) → R_6
  246. Mirror(L_6, diag1) → S_6
  247. Segment(R_6, S_6) → r_8
  248. Mirror(K_6, diag1) → T_6
  249. Mirror(Q_6, diag1) → U_6
  250. Segment(T_6, U_6) → s_8
  251. Mirror(N_6, diag1) → V_6
  252. Mirror(M_6, diag1) → W_6
  253. Mirror(M_6, diag1) → Z_6
  254. Mirror(P_1, diag1) → A_7
  255. Mirror(Q_6, diag1) → B_7
  256. Mirror(P_1, diag1) → C_7
  257. Segment(T_6, K_6) → e_8
  258. Rotate(A_4, 45°, zAxis) → D_7
  259. Rotate(G_4, 45°, zAxis) → E_7
  260. Rotate(D_4, 45°, zAxis) → F_7
  261. Rotate(O_1, 45°, zAxis) → G_7
  262. Rotate(E_4, 45°, zAxis) → H_7
  263. Rotate(D_4, 45°, zAxis) → I_7
  264. Rotate(C_4, 45°, zAxis) → J_7
  265. Rotate(A_4, 45°, zAxis) → K_7
  266. Segment(J_7, K_7) → j_9
  267. Segment(A_4, D_5) → k_9
  268. Segment(G_7, P_1) → m_9
  269. Segment(G_7, L_7) → n_9
  270. Segment(L_7, P_1) → p_9
  271. Segment(P_1, Z_1) → r_9
  272. Segment(O_1, P_1) → s_9
  273. Segment(O_1, Z_1) → t_9
  274. Vector(LO, LB) → w_3
  275. Vector(LO, RO) → u_4
  276. Vector(LB, RB) → v_5
  277. Vector(RO, RB) → w_5
  278. Rotate(RO, 45°, zAxis) → MD
  279. Point(g_4) → M_7
  280. Line(Z_1, P_1) → a_9
  281. Vector(MD1, LB) → w_6
  282. Vector(MD1, RO) → u_7
  283. Vector(LB, I_2) → v_7
  284. Vector(P_1, I_2) → w_7
  285. Intersect(p, q) → NN
  286. Plane(P_1, Z_1, (1, 0, 1)) → diag3
  287. Mirror(C_4, diag3) → N_7
  288. Mirror(A_4, diag3) → O_7
  289. Segment(N_7, O_7) → d_9
  290. Mirror(L_4, diag3) → P_7
  291. Mirror(M_4, diag3) → Q_7
  292. Segment(P_7, Q_7) → e_9
  293. Mirror(E_4, diag3) → R_7
  294. Mirror(D_4, diag3) → S_7
  295. Mirror(J_4, diag3) → T_7
  296. Mirror(K_4, diag3) → U_7
  297. Mirror(C_4, diag3) → V_7
  298. Mirror(O_1, diag3) → W_7
  299. Vector(O, NN) → v_2
  300. Vector(Q, NN) → u_2
  301. Segment(Z_1, LO) → j_{10}
  302. Vector(LO, MD) → v_8
  303. Vector(MD, T_4) → w_8
  304. Vector(P_1, T_4) → u_9
  305. Plane(P_1, Z_1, (1, 0, 1)) → diag4
  306. Segment(A_4, P_1) → l_5
  307. Segment(D_5, MD) → p_5
  308. Segment(P_1, MD) → g_9
  309. Segment(T_6, LO) → m_5
  310. Circle(LO, 0.2, m_5) → d_5
  311. Intersect(j_8, d_5) → B_8,
  312. Intersect(i_8, d_5) → C_8, D_8
  313. CircleArc(Z_7, E_8, A_8) → e_5
  314. CircleArc(H_8, G_8, F_8) → c_8
  315. Segment(A_4, G_8) → n_5
  316. Segment(F_8, B_8) → k_8
  317. Segment(E_8, D_8) → m_8
  318. Segment(D_5, A_8) → q_8
  319. Intersect(h_8, g_8) → I_8
  320. Segment(G_8, J_8) → t_8
  321. Segment(J_8, A_8) → a_8
  322. Segment(D_8, LO) → b_8
  323. Segment(LO, B_8) → d_8
  324. Vector(LO, MD) → v_4
  325. Vector(LO, P_1) → w_4
  326. Segment(L_6, J_8) → f_9
  327. Circle(MD, 0.2, p_5) → c_9
  328. Intersect(n_9, c_9) → K_8, L_8
  329. CircleArc(N_8, P_8, O_8) → h_9
  330. CircleArc(N_8, O_8, Q_8) → q_9
  331. Intersect(j_9, k_5) → R_8
  332. Segment(O_8, R_8) → i_9
  333. Segment(Q_8, L_8) → l_9
  334. Segment(P_8, M_8) → k_{10}
  335. Segment(M_8, P_1) → l_{10}
  336. Segment(MD, L_8) → m_{10}
  337. Segment(P_1, LO) → n_{10}
  338. Vector(MD, LO) → u_6
  339. Vector(Z_1, RB) → u_5
  340. Vector(P_1, RB) → u_8
  341. Segment(B_4, Z_1) → a_5
  342. Segment(A_4, P_1) → b_5
  343. CircleArc(S_8, T_8, V_8) → r_5
  344. Segment(V_8, U_8) → f_{10}
  345. Segment(P_1, U_8) → g_{10}
  346. CircleArc(S_8, Z_8, T_8) → c_{10}
  347. Segment(Z_8, W_8) → h_{10}
  348. Segment(W_8, Z_1) → i_{10}
  349. Segment(N_7, T_8) → p_{10}
  350. Segment(Z_1, P_1) → q_{10}
  351. Segment(Z_1, P_1) → r_{10}
  352. Vector(P_1, O_1) → v_6
  353. Segment(A_9, B_9) → s_{10}
  354. Segment(C_9, D_9) → t_{10}
  355. Segment((1, 0), (0, 1)) → a_{10}
  356. Segment(E_9, F_9) → b_{10}
  357. Sequence(y = nn, nn, 0, 7) → l1