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四边形内角

四边形内角
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2017-12-11 13:38
多边形角几何作图
所属专题 Mathematics Form 1
①本范例演示四边形的内角计算与性质；②涉及核心数学概念包括内角和定理、多边形几何；③作图要点：使用 GeoGebra 命令如 Circle（圆）、Segment（线段）、Intersect（交点）、Line（直线）、Angle（角度）等构建四边形并测量内角；④适合初中及以上学生学习多边形内角性质及几何作图。

GeoGebra 命令及参数

  1. Circle(Q, Saiz) → h_1
  2. Segment(P, Q) → a_1
  3. Intersect(h_1, a_1, 1) → Q_2
  4. Segment(P, S) → c_1
  5. Line(Q, c_1) → d_1
  6. Intersect(h_1, d_1, 2) → Q_1
  7. Angle(Q_1, Q, Q_2) → θ
  8. If(θ < 180°, CircleSector[Q, Q_1, Q_2], CircleSector[Q, Q_2, Q_1]) → k_1
  9. If(o < 1, 1, o) → T_2
  10. If(o > 1, 1, o) → T_1
  11. Circle(P, Saiz) → e_1
  12. Intersect(e_1, c_1, 1) → P_2
  13. Intersect(e_1, a_1, 1) → P_1
  14. Angle(P_1, P, P_2) → ε
  15. If(ε < 180°, CircleSector[P, P_1, P_2], CircleSector[P, P_2, P_1]) → p_1
  16. Circle(C, Saiz) → h
  17. Line(B, C) → m_0
  18. Intersect(h, m_0, 1) → C_2
  19. Segment(C, D) → c
  20. Intersect(h, c, 1) → C_1
  21. Segment(D, A) → d
  22. Circle(D, Saiz) → k
  23. Intersect(k, d, 1) → D_1
  24. Intersect(k, c, 1) → D_2
  25. Circle(B, Saiz) → g
  26. Intersect(g, m_0, 2) → B_2
  27. Segment(A, B) → a
  28. Intersect(g, a, 1) → B_1
  29. If(m_2 < 1, 1, m_2) → S_3
  30. If(m_2 > 1, 1, m_2) → S_4
  31. Segment(B, C) → b
  32. Point(m_0) → E
  33. Circle(A, Saiz) → f
  34. Intersect(f, a, 1) → A_1
  35. Intersect(f, d, 1) → A_2
  36. Line(D, yAxis) → l
  37. Segment(C, E) → i
  38. CircleSector(D, D_1, D_2) → q
  39. Rotate(q, (((-S_4) * 180))°, D) → q'
  40. Vector(D, A) → u_1
  41. Vector(B, A) → u_2
  42. CircleSector(B, B_2, B_1) → s
  43. Rotate(s, (((S_3 - 1) * 180))°, B) → s'
  44. Vector(C, A) → u_3
  45. If(m_2 < 0.5, 0.5, If[m_2 > 1.5, 1.5, m_2]) → S_5
  46. Translate(q', Vector[(S_4 * u_1)]) → q''
  47. CircleSector(C, C_1, C_2) → p
  48. Translate(p, Vector[((S_5 - 0.5) * u_3)]) → p'
  49. Translate(s', Vector[((S_3 - 1) * u_2)]) → s''
  50. Intersect(h, i, 1) → C_3
  51. CircleSector(C, C_3, C_1) → t
  52. Line(S, a_1) → b_1
  53. Intersect(b_1, d_1) → R
  54. Circle(S, Saiz) → f_1
  55. Circle(R, Saiz) → g_1
  56. Intersect(f_1, c_1, 1) → S_1
  57. Intersect(f_1, b_1, 2) → S_2
  58. Intersect(g_1, b_1, 1) → R_1
  59. Intersect(g_1, d_1, 1) → R_2
  60. Angle(S_1, S, S_2) → ζ
  61. Angle(R_1, R, R_2) → η
  62. If(ζ < 180°, CircleSector[S, S_1, S_2], CircleSector[S, S_2, S_1]) → q_1
  63. If(η < 180°, CircleSector[R, R_1, R_2], CircleSector[R, R_2, R_1]) → r_1
  64. Vector(Q, S) → v_1
  65. Vector(P, R) → v_2
  66. Rotate(p_1, ((T_1 * 180))°, P) → t_1
  67. Translate(t_1, Vector[(T_1 * v_2)]) → d_2
  68. Rotate(k_1, (((T_2 - 1) * 180))°, Q) → s_1
  69. Translate(s_1, Vector[((T_2 - 1) * v_1)]) → c_2
  70. Segment(S, R) → i_1
  71. Segment(Q, R) → j_1
  72. Line(A, D) → m_1
  73. Line(A, B) → n_0
  74. Line(C, D) → n_1
  75. If(x(A) > x(B), y > (Slope[n_0] * (x - x(A))) + y(A), y < (Slope[n_0] * (x - x(A))) + y(A)) → v
  76. If(x(C) > x(D), y > (Slope[n_1] * (x - x(D))) + y(D), y < (Slope[n_1] * (x - x(D))) + y(D)) → w
  77. Line(B, D) → l_1
  78. Line(A, C) → a_2
  79. If(x(C) > x(A), y > (Slope[a_2] * (x - x(A))) + y(A), y < (Slope[a_2] * (x - x(A))) + y(A)) → o_1
  80. ClosestPoint(a_2, B) → F
  81. Line(B, F) → b_2
  82. Circle(F, Ds) → e_2
  83. Intersect(e_2, b_2, 1) → G
  84. ClosestPoint(a_2, D) → H
  85. Line(H, D) → f_2
  86. Circle(H, Ds) → g_2
  87. Intersect(g_2, f_2, 2) → I
  88. ClosestPoint(l_1, C) → J
  89. Line(J, C) → h_2
  90. Circle(J, Ds) → k_2
  91. Intersect(k_2, h_2, 2) → K
  92. ClosestPoint(l_1, A) → L
  93. Line(L, A) → i_2
  94. Circle(L, Ds) → p_2
  95. Intersect(p_2, i_2, 2) → M
  96. ClosestPoint(m_0, D) → N
  97. Line(N, D) → j_2
  98. Circle(N, Ds) → q_2
  99. Intersect(q_2, j_2, 2) → O
  100. ClosestPoint(m_0, A) → T
  101. Circle(T, Ds) → r_2
  102. Line(A, T) → l_2
  103. Intersect(r_2, l_2, 1) → U
  104. ClosestPoint(m_1, B) → V
  105. Line(B, V) → n_2
  106. Circle(V, Ds) → s_2
  107. Intersect(s_2, n_2, 1) → W
  108. ClosestPoint(m_1, C) → Z
  109. Line(Z, C) → t_2
  110. Circle(Z, Ds) → c_3
  111. Intersect(c_3, t_2, 2) → E_1
  112. ClosestPoint(n_0, D) → F_1
  113. Line(F_1, D) → a_3
  114. Circle(F_1, Ds) → d_3
  115. Intersect(d_3, a_3, 2) → G_1
  116. ClosestPoint(n_0, C) → H_1
  117. Line(H_1, C) → b_3
  118. Circle(H_1, Ds) → e_3
  119. Intersect(e_3, b_3, 2) → I_1
  120. ClosestPoint(n_1, B) → J_1
  121. Line(B, J_1) → f_3
  122. Circle(J_1, Ds) → g_3
  123. Intersect(g_3, f_3, 1) → K_1
  124. ClosestPoint(n_1, A) → L_1
  125. Line(A, L_1) → h_3
  126. Circle(L_1, Ds) → k_3
  127. Intersect(k_3, h_3, 1) → M_1
  128. CircleSector(A, A_1, A_2) → r
  129. SelectedIndex(Bahasa) → nn