三角形的高、中线与角平分线综合演示

三角形的高、中线与角平分线综合演示
几何画板及绘图内容加载中,请稍等……
2014-01-14 03:05
① 本范例通过动态几何交互,直观展示三角形中高、中线与角平分线这三类重要线段的位置关系与性质。② 核心数学概念包括三角形的垂心、重心与内心,以及角平分线定理、中线性质等,涉及角度、长度和对称性。③ 作图要点:使用GeoGebra的Segment(线段)、Angle(角)、Circle(圆)、AngularBisector(角平分线)、Intersect(交点)、OrthogonalLine(垂线)、Point(点)、Midpoint(中点)、Rotate(旋转)和Polygon(多边形)等命令,构造了三角形及其辅助线,并利用多个点、线段和文本对象(如D、E、G、d、H、I等)进行标注与动态调整。④ 适合中学几何教学,尤其适用于八年级至高中阶段学习三角形性质、几何作图及动态探究,也可用于教师课堂演示或学生自主探索。

GeoGebra 命令及参数

  1. Segment(E, D) → d
  2. Segment(G, H) → g
  3. Segment(H, I) → h
  4. Segment(G, I) → i
  5. Segment(E, F) → e
  6. Segment(D, F) → f
  7. Angle(D, E, F) → δ
  8. Angle(E, F, D) → ε
  9. Angle(F, D, E) → ζ
  10. Angle(G, I, H) → η
  11. Angle(I, H, G) → θ
  12. Angle(H, G, I) → ι
  13. Circle(E, D, F) → p
  14. Circle(G, H, I) → q
  15. AngularBisector(F, E, D) → b_1
  16. AngularBisector(E, D, F) → a_1
  17. AngularBisector(D, F, E) → c_1
  18. Intersect(b_1, f) → N
  19. Segment(E, N) → d_1
  20. Intersect(a_1, e) → O
  21. Segment(D, O) → e_1
  22. Intersect(c_1, d) → P
  23. Segment(P, F) → f_1
  24. AngularBisector(G, H, I) → g_1
  25. AngularBisector(I, G, H) → h_1
  26. AngularBisector(H, I, G) → i_1
  27. Intersect(g_1, i) → Q
  28. Segment(H, Q) → j_1
  29. Intersect(i_1, g) → R
  30. Segment(I, R) → k_1
  31. Intersect(h_1, h) → S
  32. Segment(G, S) → l_1
  33. Segment(T, U) → m_1
  34. Segment(U, V) → n_1
  35. Segment(V, T) → p_1
  36. Segment(W, Z) → q_1
  37. Segment(Z, A_1) → r_1
  38. Segment(W, A_1) → s_1
  39. Circle(T, U, V) → t_1
  40. Circle(W, Z, A_1) → c_2
  41. Segment(B_1, C_1) → a_2
  42. OrthogonalLine(C_1, a_2) → b_2
  43. Point(b_2) → E_1
  44. Segment(B_1, E_1) → d_2
  45. Segment(C_1, E_1) → f_2
  46. Circle(B_1, C_1, E_1) → e_2
  47. Midpoint(a_2) → D_1
  48. Midpoint(d_2) → F_1
  49. Midpoint(f_2) → G_1
  50. Midpoint(r_1) → H_1
  51. Midpoint(q_1) → I_1
  52. Midpoint(s_1) → J_1
  53. Midpoint(m_1) → K_1
  54. Midpoint(p_1) → L_1
  55. Midpoint(n_1) → M_1
  56. Segment(U, L_1) → g_2
  57. Segment(K_1, V) → h_2
  58. Segment(M_1, T) → i_2
  59. Segment(I_1, A_1) → j_2
  60. Segment(W, H_1) → k_2
  61. Segment(Z, J_1) → l_2
  62. Segment(B_1, G_1) → m_2
  63. Segment(C_1, F_1) → n_2
  64. Segment(D_1, E_1) → p_2
  65. Intersect(g_2, h_2) → N_1
  66. Intersect(j_2, k_2) → O_1
  67. Intersect(m_2, n_2) → P_1
  68. Segment(Q_1, R_1) → q_2
  69. Segment(T_1, U_1) → t_2
  70. Segment(T_1, V_1) → a_3
  71. Segment(U_1, V_1) → b_3
  72. Segment(Z_1, A_2) → d_3
  73. Rotate(A_2, 90*°, Z_1) → B_2
  74. Angle(A_2, Z_1, B_2) → κ
  75. Segment(B_2, Z_1) → e_3
  76. Segment(B_2, A_2) → c_3
  77. Circle(T_1, U_1, V_1) → g_3
  78. Circle(B_2, Z_1, A_2) → h_3
  79. OrthogonalLine(S_1, q_2) → i_3
  80. OrthogonalLine(U_1, a_3) → p_3
  81. OrthogonalLine(T_1, b_3) → q_3
  82. OrthogonalLine(V_1, t_2) → r_3
  83. Intersect(p_3, a_3) → F_2
  84. Segment(U_1, F_2) → s_3
  85. OrthogonalLine(T_1, b_3) → t_3
  86. OrthogonalLine(V_1, t_2) → a_4
  87. Intersect(t_3, a_4) → E_2
  88. Segment(E_2, F_2) → b_4
  89. Segment(T_1, E_2) → c_4
  90. Segment(E_2, V_1) → d_4
  91. Point(d_4) → G_2
  92. Segment(T_1, G_2) → e_4
  93. Point(e_4) → H_2
  94. OrthogonalLine(V_1, c_4) → g_4
  95. OrthogonalLine(T_1, d_4) → h_4
  96. Segment(T_1, G_2) → i_4
  97. Intersect(g_4, c_4) → I_2
  98. Segment(I_2, V_1) → j_4
  99. Segment(U_1, G_2) → k_4
  100. Segment(I_2, U_1) → l_4
  101. Segment(Q_1, W_1) → r_2
  102. Segment(R_1, W_1) → s_2
  103. Circle(Q_1, R_1, W_1) → k
  104. OrthogonalLine(W_1, q_2) → a
  105. OrthogonalLine(Q_1, s_2) → b
  106. OrthogonalLine(R_1, r_2) → j
  107. Intersect(k, j, 2) → A
  108. Intersect(k, a, 2) → J
  109. Intersect(k, b, 2) → K
  110. Segment(R_1, A) → l
  111. Segment(J, W_1) → m
  112. Segment(K, Q_1) → n
  113. Intersect(r_2, l) → L
  114. Intersect(s_2, n) → M
  115. Intersect(q_2, m) → C_2
  116. Polygon(R_1, Q_1, W_1) → poly1, w_1, r_4, q_4
  117. Polygon(T_1, U_1, V_1) → poly2, v_1, t_4, u_1
  118. Segment(T_1, U_1) → r
  119. Segment(D_2, J_2) → s
  120. OrthogonalLine(D_2, s) → t
  121. Point(t) → K_2
  122. Segment(K_2, J_2) → f_3
  123. Segment(K_2, D_2) → j_3
  124. Circle(K_2, D_2, J_2) → k_3
  125. Angle(D_2, K_2, J_2) → α
  126. Angle(K_2, J_2, D_2) → β
  127. Angle(J_2, D_2, K_2) → γ
  128. Angle(G, I, R) → λ
  129. OrthogonalLine(Z_1, c_3) → c
  130. OrthogonalLine(B_2, d_3) → l_3
  131. OrthogonalLine(A_2, e_3) → m_3
  132. Intersect(c, c_3) → B
  133. Segment(Z_1, B) → n_3
  134. Segment(B_2, Z_1) → f_4
  135. Segment(Z_1, A_2) → m_4
  136. AngularBisector(j_3, f_3) → n_4, p_4
  137. AngularBisector(f_3, j_3) → s_4, a_5
  138. AngularBisector(s, j_3) → b_5, c_5
  139. AngularBisector(f_3, s) → d_5, e_5
  140. Intersect(d_5, j_3) → C
  141. Intersect(c_5, f_3) → L_2
  142. Point(n_4) → M_2
  143. Segment(K_2, M_2) → f_5
  144. Segment(L_2, D_2) → g_5
  145. Segment(C, J_2) → h_5
  146. Intersect(j_1, k_1) → N_2
  147. Intersect(d_1, e_1) → O_2
  148. Intersect(f_5, g_5) → P_2
  149. Polygon(B_2, Z_1, A_2) → poly3, a_6, b_6, z_1
  150. Polygon(T, U, V) → poly4, v, t_5, u
  151. Polygon(W, Z, A_1) → poly5, a_7, w, z
  152. Polygon(B_1, C_1, E_1) → poly6, e_6, b_7, c_6
  153. Polygon(I, G, H) → poly7, h_6, ı, g_6
  154. Polygon(E, D, F) → poly8, f_6, e_7, d_6
  155. Polygon(K_2, D_2, J_2) → poly9, j_5, k_5, d_7

AI 绘图提示语参考

绘制一个三角形ABC,连接各顶点与对边中点得到三条中线,连接各顶点与对边垂足得到三条高,连接各顶点与对边角平分线交点得到三条角平分线。通过旋转和交点操作,展示三角形的重心、垂心和内心。
以上提示语为根据原始绘图命令整理而来,仅供参考。