积极 AI Logo 积极 AI

六边形内角和与外角和定理演示

六边形内角和与外角和定理演示
几何画板及绘图内容加载中，请稍等……
2015-10-26 02:32
多边形角几何作图
所属专题 Polygons & Angles Polygons & Angles Polygons & Angles Geometry: Polygons & Angles Geometry: Polygons & Angles
①本范例通过交互式演示，向学生展示任意六边形的内角和为720度，外角和为360度的几何现象；②涉及的核心数学概念包括多边形内角和定理、外角和定理、角度计算；③作图要点——从下方『构造摘要』提炼用到了Segment（线段）、Circle（圆）、Intersect（交点）、Ray（射线）、CircleSector（扇形）、Vector（向量）、Translate（平移）、Mirror（镜像）、Dilate（缩放）、If（条件）、Rotate（旋转）、Polygon（多边形）、Point（点）等GeoGebra命令/对象；④适合初中及以上数学学习者，用于理解和验证多边形角度性质，增强空间想象能力。

GeoGebra 命令及参数

  1. Segment(C, A_1) → i_3
  2. Circle(C, 1.5) → h
  3. Intersect(h, i_3) → L,
  4. Ray(C, D) → c
  5. Intersect(h, c, 1) → P
  6. Ray(A, B) → a
  7. Ray(B, C) → b
  8. Ray(E, A) → e
  9. Circle(A, 1.5) → f
  10. Circle(B, 1.5) → g
  11. Circle(D, 1.5) → k
  12. Circle(E, 1.5) → p
  13. Segment(C, A) → i
  14. Segment(C, E) → j
  15. Intersect(f, a, 1) → F
  16. Intersect(f, i, 1) → G
  17. Intersect(f, e, 1) → H
  18. Intersect(f, e, 2) → I
  19. Intersect(p, e) → J,
  20. Intersect(p, j) → K,
  21. Intersect(k, c, 2) → O
  22. Intersect(h, j, 1) → Q
  23. Intersect(h, i, 1) → R
  24. Intersect(h, b, 1) → S
  25. Intersect(g, a, 2) → T
  26. Intersect(g, b, 1) → U
  27. Intersect(g, a, 1) → V
  28. CircleSector(A, F, G) → q
  29. CircleSector(A, G, H) → r
  30. CircleSector(B, U, V) → s
  31. CircleSector(C, Q, R) → c_1
  32. CircleSector(C, R, S) → d_1
  33. Intersect(k, c, 1) → W
  34. CircleSector(E, J, K) → h_1
  35. CircleSector(A, I, F) → p_1
  36. CircleSector(B, T, U) → q_1
  37. Intersect(h, b, 2) → Z
  38. CircleSector(C, Z, P) → r_1
  39. Vector(A, B) → u
  40. Vector(C, B) → v
  41. Vector(E, D) → w
  42. Vector(C, D) → u_1
  43. Vector(C, E) → v_1
  44. Vector(A, E) → w_1
  45. Translate(q, u) → q'
  46. Translate(d_1, v) → s_1
  47. Mirror(s_1, B) → t_1
  48. Dilate(A, If[0 < l ≤ 1, 1 - l, 0], B) → A'
  49. Dilate(C, If[0 < l ≤ 1, 1 - l, 0], B) → C'
  50. Dilate(A, If[1 < l ≤ 2, 2 - l, 0], E) → A'_1
  51. Dilate(C, If[1 < l ≤ 2, 2 - l, 0], E) → C'_1
  52. Dilate(C, If[2 < l ≤ 3, 3 - l, 0], D) → C'_2
  53. Dilate(E, If[2 < l ≤ 3, 3 - l, 0], D) → E'
  54. Vector(A, B) → a_1
  55. Vector(C, C') → b_1
  56. Vector(A, A'_1) → i_1
  57. Vector(E, E') → j_1
  58. Vector(C, C'_2) → l_1
  59. Vector(C, C'_1) → m_1
  60. Translate(d_1, b_1) → c_2
  61. Translate(r, i_1) → r'_1
  62. Translate(r, w_1) → r'_2
  63. Translate(c_1, v_1) → f_2
  64. Translate(c_1, m_1) → g_2
  65. CircleSector(C, P, L) → t
  66. Translate(t, u_1) → t'
  67. Translate(t, l_1) → t'_1
  68. Translate(q, a_1) → r'
  69. Translate(d_1, b_1) → h_2
  70. If(0 < l < 1, Rotate[h_2, ((l * 180))°, C']) → k_2
  71. Vector(A, A') → n_1
  72. Translate(q, n_1) → q'_1
  73. Mirror(r'_2, E) → p_2
  74. If(1 < l < 2, Rotate[r'_1, (((l - 1) * 180))°, A'_1]) → q_2
  75. Segment(E, C) → i_2
  76. Vector(D, C) → u_2
  77. Vector(E, C) → v_2
  78. Vector(A, C) → w_2
  79. Vector(B, C) → l_2
  80. Dilate(B, If[0 < o < 1, 1 - o, 0], C) → B'
  81. Dilate(A, If[1 < o < 2, 2 - o, 0], C) → A'_2
  82. Dilate(E, If[2 < o < 3, 3 - o, 0], C) → E'_1
  83. Dilate(D, If[3 < o < 4, 4 - o, 0], C) → D'
  84. Vector(B, B') → m_2
  85. Vector(A, A'_2) → n_2
  86. Vector(E, E'_1) → s_2
  87. Vector(D, D') → t_2
  88. Translate(q_1, m_2) → c_3
  89. Translate(q_1, l_2) → d_3
  90. Translate(p_1, w_2) → e_3
  91. If(1 < o < 2, Translate[p_1, n_2]) → h_3
  92. Ray(D, A_1) → a_3
  93. Ray(A_1, E) → b_3
  94. Circle(A_1, 1.5) → q_3
  95. Intersect(q_3, i_3) → M,
  96. Intersect(q_3, b_3, 1) → N
  97. Intersect(q_3, a_3, 2) → B_1
  98. Intersect(k, c, 2) → C_1
  99. Intersect(k, a_3, 1) → D_1
  100. Intersect(k, c, 1) → E_1
  101. CircleSector(C, L, Q) → d
  102. Intersect(p, b_3, 1) → F_1
  103. Intersect(p, i_2) → G_1,
  104. CircleSector(E, G_1, N) → e_1
  105. Dilate(E, If[2 < l < 3, 3 - l, 0], A_1) → E'_2
  106. Dilate(C, If[2 < l < 3, 3 - l, 0], A_1) → C'_3
  107. Dilate(C, If[3 < l < 4, 4 - l, 0], D) → C'_4
  108. Dilate(A_1, If[3 < l < 4, 4 - l, 0], D) → H_1
  109. Vector(E, A_1) → f_1
  110. Vector(C, A_1) → g_1
  111. Translate(e_1, f_1) → k_1
  112. Translate(d, g_1) → d'
  113. Vector(E, E'_2) → a_2
  114. Vector(C, C'_3) → b_2
  115. Translate(e_1, a_2) → d_2
  116. Translate(d, b_2) → d'_1
  117. Rotate(d_2, If[2 < l < 3, (((l - 2) * 180))°, 0], E'_2) → e_2
  118. Mirror(k_1, A_1) → r_2
  119. CircleSector(A_1, N, M) → f_3
  120. Intersect(q_3, a_3, 1) → I_1
  121. CircleSector(A_1, M, I_1) → g_3
  122. CircleSector(D, D_1, E_1) → k_3
  123. Vector(C, D) → j_2
  124. Vector(A_1, D) → u_3
  125. Translate(g_3, u_3) → p_3
  126. Translate(t, j_2) → t'_2
  127. Mirror(p_3, D) → r_3
  128. Vector(A_1, H_1) → v_3
  129. Vector(C, C'_4) → w_3
  130. Translate(g_3, v_3) → s_3
  131. Translate(t, w_3) → t'_3
  132. Rotate(s_3, If[3 < l < 4, (((l - 3) * 180))°, 0], H_1) → t_3
  133. Intersect(p, b_3, 2) → J_1
  134. Polygon(A, B, C) → poly1, c_4, a_4, b_4
  135. Polygon(A, C, E) → poly2, e_4, a_5, c_5
  136. Polygon(E, C, A_1) → poly3, a_6, e_5, c_6
  137. Polygon(A_1, C, D) → poly4, d_4, a_7, c_7
  138. Polygon(A, B, C, D, A_1, E) → poly5, a_8, b_5, c_8, d_5, a_9, e_6
  139. Intersect(e, e_6) → K_1
  140. Intersect(p, e, 1) → L_1
  141. CircleSector(E, J_1, L_1) → f_4
  142. CircleSector(A_1, B_1, N) → g_4
  143. CircleSector(D, C_1, D_1) → h_4
  144. Vector(E, C) → j_3
  145. Vector(A_1, C) → l_3
  146. Vector(D, C) → m_3
  147. Translate(f_4, j_3) → k_4
  148. Translate(g_4, l_3) → p_4
  149. Translate(h_4, m_3) → q_4
  150. Dilate(E, If[2 < o < 3, 3 - o, 0], C) → E'_3
  151. Dilate(A_1, If[3 < o < 4, 4 - o, 0], C) → M_1
  152. Dilate(D, If[4 < o < 5, 5 - o, 0], C) → D'_1
  153. Vector(E, E'_3) → n_3
  154. Vector(A_1, M_1) → u_4
  155. Vector(D, D'_1) → v_4
  156. If(2 < o < 3, Translate[f_4, n_3]) → r_4
  157. If(3 < o < 4, Translate[g_4, u_4]) → s_4
  158. If(4 < o < 5, Translate[h_4, v_4]) → t_4
  159. Ray(C, A_1) → l_4
  160. Ray(C, E) → m_4
  161. Point(l_4) → N_1
  162. Point(m_4) → O_1
  163. Ray(A_1, N_1) → i_4
  164. Ray(E, O_1) → j_4