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矩形与菱形的性质

矩形与菱形的性质
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2019-07-12 00:38
多边形不等式几何作图
所属专题 Calculating areas as an approach to the notions of limit and
该范例演示了矩形和菱形的性质，涉及几何中的对称性和相似性。通过使用GeoGebra命令如Line, Intersect, Midpoint等，可以构造矩形和菱形，并探索它们的性质。适合初中和高中学生学习几何作图和性质探索。

GeoGebra 命令及参数

  1. Line(p, q) → f
  2. Intersect(c, f, 1) → A
  3. Intersect(c, f, 2) → C
  4. Line(C, xAxis) → g
  5. Intersect(c, g, 2) → B
  6. Midpoint(B, C) → D
  7. Intersect(c, yAxis) → E,
  8. Distance(D, E) → distantziaDE
  9. Circle(D, 0.28201) → d
  10. Circle(D, (0.28201 * 2)) → e
  11. Circle(D, (3 * 0.28201)) → h
  12. Circle(D, (4 * 0.28201)) → k
  13. Circle(D, (5 * 0.28201)) → r
  14. Circle(D, (6 * 0.280201)) → s
  15. Circle(D, (7 * 0.28201)) → t
  16. Circle(D, (8 * 0.28201)) → c_1
  17. Circle(D, (9 * 0.28201)) → d_1
  18. Intersect(d, yAxis, 2) → F
  19. Intersect(e, yAxis, 2) → G
  20. Intersect(h, yAxis, 2) → H
  21. Intersect(k, yAxis, 2) → I
  22. Intersect(t, yAxis, 2) → M
  23. Intersect(c_1, yAxis, 2) → N
  24. Intersect(d_1, yAxis, 2) → O
  25. Intersect(r, yAxis) → J, K
  26. Line(F, g) → i
  27. Line(G, i) → j
  28. Line(H, j) → l
  29. Line(I, l) → m
  30. Line(K, m) → n
  31. Intersect(c, i) → P, Q
  32. Intersect(c, j) → R, S
  33. Intersect(c, l) → T, U
  34. Intersect(c, m) → V, W
  35. Intersect(c, n) → Z, A_1
  36. OrthogonalLine(P, i) → i_1
  37. OrthogonalLine(R, j) → j_1
  38. OrthogonalLine(T, l) → k_1
  39. OrthogonalLine(V, m) → l_1
  40. OrthogonalLine(Z, n) → m_1
  41. OrthogonalLine(A_1, n) → e_1
  42. OrthogonalLine(W, m) → f_2
  43. OrthogonalLine(U, l) → g_2
  44. OrthogonalLine(S, j) → h_2
  45. OrthogonalLine(Q, i) → i_2
  46. Intersect(g, i_1) → J_1
  47. Intersect(g, i_2) → K_1
  48. Polygon(P, J_1, K_1, Q) → Laukia1, p_2, j_2, k_2, q_2
  49. Intersect(i, j_1) → L_1
  50. Intersect(i, h_2) → M_1
  51. Polygon(R, L_1, M_1, S) → Laukia2, r_2, l_2, m_2, s_2
  52. Intersect(j, k_1) → N_1
  53. Intersect(j, g_2) → O_1
  54. Polygon(T, N_1, O_1, U) → Laukia3, t_2, n_2, o_1, u
  55. Intersect(l, l_1) → P_1
  56. Intersect(l, f_2) → Q_1
  57. Polygon(V, P_1, Q_1, W) → Laukia4, v, a_2, b_2, w
  58. Intersect(m, m_1) → R_1
  59. Intersect(m, e_1) → S_1
  60. Polygon(Z, R_1, S_1, A_1) → Laukia5, z_1, c_2, d_2, e_2
  61. PointIn(Laukia1) → PuntuaLaukia1_1
  62. PointIn(Laukia2) → PuntuaLaukia2_1
  63. PointIn(Laukia3) → PuntuaLaukia3_1
  64. PointIn(Laukia4) → PuntuaLaukia4
  65. PointIn(Laukia5) → PuntuaLaukia5
  66. OrthogonalLine(B, j_2) → t_3
  67. Intersect(f, t_3) → F_2
  68. OrthogonalLine(F_2, t_3) → a_3
  69. Intersect(c, a_3, 2) → G_2
  70. Polygon(B, C, F_2) → Triangelua1, b_3, b_4, c_3
  71. Polygon(F_2, G_2, B) → Triangelua2, b_5, d_3, e_3
  72. Polygon(F_2, A, G_2) → Triangelua3, f_4, g_4, a_4
  73. PointIn(Triangelua1) → PuntuaTriangelua1
  74. PointIn(Triangelua2) → PuntuaTriangelua2
  75. PointIn(Triangelua3) → PuntuaTriangelua3
  76. Intersect(g, j_2) → H_2
  77. Intersect(g, j_2) → I_2
  78. Intersect(g, j_2) → J_2
  79. Intersect(g, k_2) → K_2
  80. Intersect(c, k_2, 1) → L_2
  81. Polygon(L_2, K_2, C) → Triangelua4, c_4, h_4, i_4
  82. Circle(D, (6 * 0.28201)) → d_4
  83. Intersect(d_4, yAxis) → L, B_1
  84. Distance(M, B_1) → distantziaMB1
  85. Line(B_1, n) → a
  86. Line(M, a) → b
  87. Line(N, b) → f_1
  88. Line(O, f_1) → g_1
  89. Intersect(c, a) → C_1, D_1
  90. Intersect(c, b) → E_1, F_1
  91. Intersect(c, f_1) → G_1, H_1
  92. OrthogonalLine(C_1, n) → h_1
  93. OrthogonalLine(E_1, a) → n_1
  94. OrthogonalLine(G_1, b) → p_1
  95. OrthogonalLine(H_1, f_1) → q_1
  96. OrthogonalLine(F_1, b) → r_1
  97. OrthogonalLine(D_1, a) → s_1
  98. Intersect(n, h_1) → I_1
  99. Intersect(n, s_1) → T_1
  100. Polygon(C_1, I_1, T_1, D_1) → Laukia6, t_1, a_1, b_1, f_3
  101. Intersect(a, n_1) → U_1
  102. Intersect(a, r_1) → V_1
  103. Polygon(E_1, U_1, V_1, F_1) → Laukia7, g_3, u_1, v_1, h_3
  104. Intersect(b, p_1) → W_1
  105. Intersect(b, q_1) → Z_1
  106. Polygon(G_1, W_1, Z_1, H_1) → Laukia8, i_3, w_1, j_3, k_3
  107. Line(E, g_1) → l_3
  108. Intersect(q_1, l_3) → A_2
  109. Intersect(p_1, l_3) → B_2
  110. PointIn(Laukia6) → PuntuaLaukia6
  111. PointIn(Laukia7) → PuntuaLaukia7
  112. PointIn(Laukia8) → PuntuaLaukia8
  113. Intersect(c, g_1) → C_2, D_2
  114. OrthogonalLine(C_2, g_1) → m_3
  115. OrthogonalLine(D_2, g_1) → n_3
  116. Intersect(m_3, l_3) → E_2
  117. Intersect(f_1, m_3) → M_2
  118. Intersect(f_1, n_3) → N_2
  119. Intersect(l_3, n_3) → O_2
  120. Polygon(E_2, M_2, N_2, O_2) → Laukia9, p_3, q_3, r_3, s_3
  121. PointIn(Laukia9) → PuntuaLaukia9
  122. PointIn(Laukia2) → PuntuaLaukia2
  123. PointIn(Laukia3) → PuntuaLaukia3
  124. PointIn(Laukia1) → PuntuaLaukia1
  125. PointIn(Triangelua4) → PuntuaTriangelua4
  126. Intersect(c, p_3) → P_2,
  127. Intersect(c, r_3) → Q_2,
  128. Polygon(P_2, M_2, N_2, Q_2) → Laukia10, l_4, m_4, n_4, p_4
  129. Intersect(s_3, p_3) → R_2
  130. Polygon(P_2, R_2, O_2, Q_2) → Laukia11, q_4, r_4, s_4, t_4
  131. PointIn(Laukia10) → PuntuaLaukia10
  132. PointIn(Laukia11) → PuntuaLaukia11