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Basic Geometric Constructions Example

Basic Geometric Constructions Example
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2015-09-25 00:45
CirclePolygonAngleGeometric Construction
This example demonstrates the process of constructing basic geometric figures using GeoGebra, involving core mathematical concepts such as geometric construction, angle measurement, and graphical transformations. Key GeoGebra commands and objects used include Segment, Rotate, Angle, Point, Circle, Intersect, AttachCopyToView, and Ellipse, making it suitable for middle school and above students to learn and understand fundamental geometric construction methods, ideal for classroom teaching or homework practice.

GeoGebra Commands & Parameters

  1. Segment(A_1, B_1) → a
  2. Segment(X_1, Y_1) → b
  3. Rotate(C_1, 32*°, B_2) → A_2
  4. Angle(C_1, B_2, A_2) → α
  5. Segment(B_2, A_2) → c
  6. Segment(B_2, C_1) → d
  7. Rotate(C, 45*°, B_3) → A_3
  8. Angle(C, B_3, A_3) → β
  9. Segment(B_3, A_3) → e
  10. Segment(B_3, C) → f
  11. Segment(A_4, B) → g
  12. Rotate(D, 60*°, A) → D'
  13. Angle(D, A, D') → γ
  14. Segment(A, D') → h
  15. Segment(A, D) → i
  16. Rotate(Z, 120*°, Y) → X
  17. Angle(Z, Y, X) → δ
  18. Segment(X, Y) → j
  19. Segment(Y, Z) → k
  20. Point(g) → E
  21. Circle(A_4, Segment[E, A_4]) → p
  22. Circle(B, Segment[A_4, E]) → q
  23. Intersect(p, q, 1) → F
  24. Intersect(p, q, 2) → G
  25. Segment(F, G) → l
  26. Angle(g, l) → ε
  27. AttachCopyToView(PolyLine[(14.266727717871698, -29.20442136434609), (15.212743824201402, -29.393624585612024), (16.300662346480564, -29.630128612194447), (16.44256476243002, -29.67742941751093), (17.577784090025666, -29.819331833460385), (20.841539656863144, -30.43424230257468), (22.307864621674188, -30.954551161056006), (22.544368648256615, -31.09645357700546), (22.5916694535731, -31.42755921422085), (22.638970258889586, -33.41419303751319), (22.638970258889586, -35.211623639539596), (22.40246623230716, -35.4954284714385), (21.97675898445879, -35.826534108653895), (21.551051736610425, -36.06303813523631), (21.125344488762057, -36.1103389405528), (19.375214692052104, -36.25224135650225), (16.773670399645415, -35.96843652460335), (15.63845107204977, -35.40082686080553), (15.591150266733285, -35.25892444485608), (15.685751877366256, -35.44812766612202), (15.874955098632196, -35.87383491397038), (16.91557281559487, -38.19157437447811), (17.199377647493783, -38.617281622326466), (17.81428811660809, -38.75918403827592), (18.476499391038885, -38.80648484359241), (19.044109054836706, -38.71188323295944), (19.375214692052104, -38.617281622326466), (19.89552355053344, -38.19157437447811), (20.557734824964236, -36.867151825616546), (20.88884046217963, -35.92113571928686), (20.841539656863144, -35.59003008207147), (20.79423885154666, -35.30622525017257), (20.60503563028072, -35.02242041827366), (20.51043401964775, -34.83321719700772), (20.368531603698294, -34.69131478105827), (19.848222745216955, -34.31290833852639), (19.186011470786163, -33.83990028536155), (19.044109054836706, -33.6979978694121), (18.80760502825428, -33.50879464814616), (18.23999536445646, -33.17768901093077), (18.00349133787403, -33.03578659498132), (17.766987311291604, -32.799282568398894), (17.34128006344324, -32.51547773649999), (16.773670399645415, -32.08977048865163), (16.300662346480564, -31.711364046119755), (15.969556709265166, -31.52216082485382), (15.780353487999225, -31.380258408904368), (15.118142213568433, -30.812648745106554), (14.64513416040358, -30.386941497258196), (14.45593093913764, -30.197738275992258), (14.361329328504668, -30.00853505472632), (14.219426912555212, -29.7720310281439), (14.124825301922243, -29.488226196244995), (14.030223691289272, -29.299022974979056), (NaN, NaN), (12.75310194774417, -40.9350210828342), (12.516597921161745, -40.887720277517715), (12.138191478629862, -40.887720277517715), (11.901687452047437, -40.9350210828342), (11.712484230781495, -40.982321888150686), (11.523281009515555, -41.07692349878365), (11.334077788249614, -41.26612672004959), (11.192175372300158, -41.50263074663201), (11.097573761667187, -41.69183396789795), (11.097573761667187, -41.881037189163884), (11.097573761667187, -42.070240410429825), (11.144874566983672, -42.25944363169576), (11.286776982933128, -42.448646852961694), (11.428679398882585, -42.59054926891115), (11.617882620148524, -42.7324516848606), (11.901687452047437, -42.92165490612654), (12.090890673313377, -42.96895571144302), (12.232793089262833, -43.01625651675951), (12.374695505212289, -43.063557322075994), (12.516597921161745, -43.01625651675951), (12.6585003371112, -42.96895571144302), (12.800402753060656, -42.87435410081006), (12.989605974326597, -42.7324516848606), (13.131508390276052, -42.59054926891115), (13.178809195592537, -42.40134604764521), (13.226110000909022, -42.022939605113336), (13.226110000909022, -41.69183396789795), (13.226110000909022, -41.408029135999044), (13.178809195592537, -41.2188259147331), (13.131508390276052, -41.07692349878365), (13.036906779643083, -40.9350210828342), (12.895004363693626, -40.84041947220123), (NaN, NaN), (17.53048328470918, -42.022939605113336), (17.152076842177298, -42.11754121574631), (16.91557281559487, -42.25944363169576), (16.72636959432893, -42.40134604764521), (16.537166373062988, -42.59054926891115), (16.44256476243002, -42.7324516848606), (16.34796315179705, -42.87435410081006), (16.34796315179705, -43.110858127392476), (16.34796315179705, -43.30006134865842), (16.44256476243002, -43.678467791190286), (16.63176798369596, -43.9622726230892), (16.8209712049619, -44.198776649671615), (17.104776036860812, -44.48258148157052), (17.293979258126754, -44.62448389751997), (17.483182479392696, -44.71908550815294), (17.672385700658634, -44.71908550815294), (17.861588921924575, -44.67178470283646), (18.050792143190517, -44.52988228688701), (18.23999536445646, -44.293378260304586), (18.381897780405914, -44.05687423372216), (18.52380019635537, -43.77306940182326), (18.61840180698834, -43.44196376460787), (18.61840180698834, -43.25276054334193), (18.571101001671856, -43.01625651675951), (18.476499391038885, -42.82705329549357), (18.4291985857224, -42.68515087954412), (18.287296169772944, -42.59054926891115), (18.192694559139973, -42.40134604764521), (18.050792143190517, -42.21214282637928), (17.90888972724106, -42.11754121574631), (17.766987311291604, -42.070240410429825), (17.625084895342148, -42.11754121574631), (NaN, NaN), (12.611199531794714, -42.21214282637928), (12.421996310528774, -42.11754121574631), (12.280093894579318, -42.022939605113336), (12.421996310528774, -41.881037189163884), (12.56389872647823, -41.73913477321443), (12.705801142427685, -41.69183396789795), (12.895004363693626, -41.8337363838474), (12.989605974326597, -42.022939605113336), (12.942305169010112, -42.16484202106279), (12.895004363693626, -42.30674443701224), (12.705801142427685, -42.40134604764521), (12.516597921161745, -42.40134604764521), (12.421996310528774, -42.21214282637928), (12.374695505212289, -42.070240410429825), (NaN, NaN), (17.01017442622784, -43.3473621539749), (16.91557281559487, -43.48926456992435), (16.868272010278385, -43.678467791190286), (16.91557281559487, -43.86767101245623), (17.057475231544327, -44.05687423372216), (17.199377647493783, -44.246077454988104), (17.293979258126754, -44.387979870937556), (17.43588167407621, -44.293378260304586), (17.53048328470918, -44.10417503903865), (17.672385700658634, -43.86767101245623), (17.766987311291604, -43.678467791190286), (17.71968650597512, -43.53656537524083), (17.625084895342148, -43.39466295929138), (17.483182479392696, -43.30006134865842), (17.34128006344324, -43.3473621539749), (17.199377647493783, -43.44196376460787), (17.152076842177298, -43.58386618055732), (17.199377647493783, -43.77306940182326), (17.24667845281027, -43.91497181777271), true], 1, (-23.95232297784837, -52.9967264385377), (40.660577084470454, -24.42704002738117), (0, 604), (1366, 0)) → stroke1
  28. Segment(I, J) → m
  29. Point(m) → K
  30. Circle(I, Segment[I, K]) → r
  31. Circle(J, Segment[I, K]) → s
  32. Intersect(r, s, 1) → L
  33. Intersect(r, s, 2) → M
  34. Segment(L, M) → n
  35. Angle(m, n) → ζ
  36. Ellipse(N, O, P) → t
  37. Ellipse(Q, R, S) → c_1
  38. Circle(T, U) → d_1
  39. Ellipse(V, W, D_1) → e_1
  40. Ellipse(E_1, F_1, G_1) → f_1
  41. Intersect(m, n) → H_1
  42. Point(m) → I_1
  43. Circle(H_1, Segment[H_1, I_1]) → g_1
  44. Circle(J, Segment[H_1, I_1]) → h_1
  45. Intersect(g_1, h_1, 1) → J_1
  46. Intersect(g_1, h_1, 2) → K_1
  47. Segment(J_1, K_1) → a_1
  48. Intersect(m, a_1) → L_1
  49. Point(i) → M_1
  50. Circle(A, Segment[A, M_1]) → k_1
  51. Intersect(k_1, h, 1) → N_1
  52. Circle(N_1, Segment[N_1, M_1]) → p_1
  53. Circle(M_1, Segment[M_1, N_1]) → q_1
  54. Intersect(p_1, q_1, 1) → O_1
  55. Point(k) → P_1
  56. Circle(Y, Segment[Y, P_1]) → r_1
  57. Intersect(r_1, j, 1) → Q_1
  58. Circle(P_1, Segment[Q_1, P_1]) → s_1
  59. Circle(Q_1, Segment[Q_1, P_1]) → t_1
  60. Intersect(s_1, t_1, 2) → R_1
  61. Segment(Y, R_1) → b_1
  62. Circle(T_1, Segment[S_1, T_1]) → c_2
  63. Point(c_2) → U_1
  64. Circle(U_1, Segment[T_1, U_1]) → d_2
  65. Point(d_2) → V_1
  66. Circle(V_1, Segment[U_1, V_1]) → e_2
  67. Point(e_2) → W_1
  68. Circle(W_1, Segment[V_1, W_1]) → f_2
  69. Intersect(c_2, d_2, 2) → Z_1
  70. Intersect(d_2, e_2, 2) → C_2
  71. Intersect(e_2, f_2, 2) → D_2
  72. Intersect(e_2, f_2, 1) → E_2
  73. Intersect(d_2, e_2, 1) → F_2
  74. Intersect(c_2, d_2, 1) → G_2
  75. Circle(E_2, Segment[E_2, F_2]) → g_2
  76. Circle(F_2, Segment[E_2, F_2]) → h_2
  77. Circle(G_2, Segment[F_2, G_2]) → k_2
  78. Circle(C_2, Segment[Z_1, C_2]) → p_2
  79. Circle(Z_1, Segment[C_2, Z_1]) → q_2
  80. Circle(D_2, Segment[C_2, D_2]) → r_2
  81. Intersect(h_2, k_2, 2) → H_2
  82. Intersect(g_2, h_2, 2) → I_2
  83. Intersect(p_2, r_2, 2) → J_2
  84. Circle(H_2, Segment[I_2, H_2]) → s_2
  85. Circle(I_2, Segment[I_2, H_2]) → t_2
  86. Intersect(p_2, q_2, 1) → K_2
  87. Circle(J_2, Segment[K_2, J_2]) → c_3
  88. Circle(K_2, Segment[J_2, K_2]) → d_3
  89. Intersect(s_2, t_2, 1) → L_2
  90. Intersect(k_2, s_2, 1) → M_2
  91. Intersect(c_2, k_2, 1) → N_2
  92. Intersect(c_2, q_2, 2) → O_2
  93. Intersect(q_2, d_3, 2) → P_2
  94. Intersect(c_3, d_3, 1) → Q_2
  95. Intersect(r_2, c_3, 1) → R_2
  96. Intersect(f_2, r_2, 1) → S_2
  97. Intersect(f_2, g_2, 2) → T_2
  98. Intersect(g_2, t_2, 2) → U_2
  99. Circle(M_2, Segment[L_2, H_2]) → e_3
  100. Circle(N_2, Segment[G_2, N_2]) → f_3
  101. Circle(L_2, Segment[U_1, T_1]) → g_3
  102. Circle(U_2, Segment[I_2, U_2]) → h_3
  103. Circle(T_2, Segment[E_2, T_2]) → k_3
  104. Circle(S_2, Segment[W_1, S_2]) → p_3
  105. Circle(R_2, Segment[D_2, R_2]) → q_3
  106. Circle(Q_2, Segment[J_2, Q_2]) → r_3
  107. Circle(P_2, Segment[K_2, P_2]) → s_3
  108. Circle(O_2, Segment[Z_1, O_2]) → t_3
  109. Circle(S_1, Segment[T_1, S_1]) → c_4
  110. Intersect(f_2, k_3, 2) → V_2
  111. Circle(V_2, Segment[U_2, T_2]) → d_4
  112. Intersect(s_2, e_3, 2) → W_2
  113. Intersect(t_2, g_3, 2) → Z_2
  114. Intersect(d_3, r_3, 2) → C_3
  115. Intersect(c_3, q_3, 2) → D_3
  116. Circle(W_2, Segment[W_2, L_2]) → e_4
  117. Circle(Z_2, Segment[L_2, Z_2]) → f_4
  118. Circle(D_3, Segment[R_2, D_3]) → g_4
  119. Circle(C_3, Segment[C_3, Q_2]) → h_4