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三角形特殊线段概述

三角形特殊线段概述
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2020-01-22 00:04
测试改名0解析几何几何作图
①本范例演示了三角形中的角平分线、中线、高线等特殊线段的性质与关系；②涉及核心数学概念包括向量、坐标几何、不等式、几何作图等；③构造过程中运用了Segment（线段）、Vector（向量）、Translate（平移）、AngularBisector（角平分线）、Intersect（交点）、OrthogonalLine（垂线）、Circle（圆）、Midpoint（中点）、Polygon（多边形）、Angle（角度）、Line（直线）、Center（中心）等命令与对象；④适合高中数学教学与几何作图学习。

GeoGebra 命令及参数

  1. Segment(B, A) → a
  2. Segment(A, C) → b
  3. Segment(C, B) → e
  4. Vector(C, H) → v
  5. Vector(C, J) → w
  6. Vector(C, I) → z
  7. Vector(C, C_2) → u
  8. Translate(B, u) → K
  9. Translate(C, u) → L
  10. Translate(A, u) → M
  11. Translate(B, u) → E'
  12. Translate(A, u) → G'
  13. Segment(E', G') → f
  14. Translate(A, u) → G'_1
  15. Translate(C, u) → F'
  16. Segment(G'_1, F') → g
  17. Translate(C, u) → F'_1
  18. Translate(B, u) → E'_1
  19. Segment(F'_1, E'_1) → h
  20. Translate(B, w) → D
  21. Translate(C, w) → N
  22. Translate(A, w) → O
  23. Translate(B, v) → P
  24. Translate(C, v) → Q
  25. Translate(A, v) → R
  26. Translate(C, v) → F'_2
  27. Translate(B, v) → E'_2
  28. Segment(F'_2, E'_2) → d
  29. Translate(B, v) → E'_3
  30. Translate(A, v) → G'_2
  31. Segment(E'_3, G'_2) → i
  32. Translate(A, v) → G'_3
  33. Translate(C, v) → F'_3
  34. Segment(G'_3, F'_3) → j
  35. Translate(C, w) → F'_4
  36. Translate(B, w) → E'_4
  37. Segment(F'_4, E'_4) → k
  38. Translate(B, w) → E'_5
  39. Translate(A, w) → G'_4
  40. Segment(E'_5, G'_4) → l
  41. Translate(A, w) → G'_5
  42. Translate(C, w) → F'_5
  43. Segment(G'_5, F'_5) → m
  44. Translate(B, z) → S
  45. Translate(B, z) → E'_6
  46. Translate(A, z) → G'_6
  47. Segment(E'_6, G'_6) → n
  48. Translate(A, z) → T
  49. Translate(C, z) → U
  50. Translate(C, z) → F'_6
  51. Translate(B, z) → E'_7
  52. Segment(F'_6, E'_7) → p
  53. Translate(A, z) → G'_7
  54. Translate(C, z) → F'_7
  55. Segment(G'_7, F'_7) → q
  56. AngularBisector(U, S, G'_6) → r
  57. AngularBisector(T, U, S) → s
  58. AngularBisector(S, T, U) → t
  59. Intersect(p, t) → V
  60. Intersect(n, s) → W
  61. Intersect(q, r) → Z
  62. Intersect(r, s) → A1
  63. Segment(S, Z) → a1
  64. Segment(U, W) → b1
  65. Segment(T, V) → c1
  66. OrthogonalLine(A1, q) → d1
  67. Intersect(q, d1) → B1
  68. Circle(A1, B1) → e1
  69. Midpoint(k) → M1
  70. Midpoint(l) → N1
  71. Midpoint(m) → O1
  72. Segment(D, O1) → l1
  73. Segment(N, N1) → m1
  74. Segment(O, M1) → n1
  75. Intersect(l1, m1) → P1
  76. Polygon(B, A, C) → poly1, f_1, e_1, g_1
  77. Angle(poly1) → α, β, γ
  78. Line(K, M) → a_1
  79. Line(M, L) → b_1
  80. Line(L, K) → c_1
  81. OrthogonalLine(K, b_1) → d_1
  82. OrthogonalLine(L, a_1) → h_1
  83. OrthogonalLine(M, c_1) → i_1
  84. Intersect(d_1, h_1) → D_1
  85. Circle(P, Q, R) → k_1
  86. Center(k_1) → E_1
  87. OrthogonalLine(E_1, i) → j_1
  88. OrthogonalLine(E_1, d) → l_1
  89. OrthogonalLine(E_1, j) → m_1
  90. Intersect(d, l_1) → F_1
  91. Intersect(i, j_1) → G_1
  92. Intersect(j, m_1) → H_1
  93. Segment(F_1, E_1) → n_1
  94. Segment(E_1, H_1) → p_1
  95. Segment(E_1, G_1) → q_1
  96. OrthogonalLine(D_1, b_1) → r_1
  97. OrthogonalLine(D_1, a_1) → s_1
  98. OrthogonalLine(D_1, c_1) → t_1
  99. Intersect(t_1, c_1) → A_1
  100. Intersect(r_1, b_1) → B_1
  101. Intersect(s_1, a_1) → C_1
  102. Segment(D_1, C_1) → a_2
  103. Segment(D_1, B_1) → b_2
  104. Segment(D_1, A_1) → c_2
  105. Segment(K, D_1) → d_2
  106. Segment(L, D_1) → e_2
  107. Segment(M, D_1) → f_2
  108. Segment(L, B_1) → g_2
  109. Segment(L, A_1) → h_2
  110. Segment(M, C_1) → i_2
  111. Translate(B, v) → E'_8
  112. Translate(A, v) → G'_8
  113. Translate(C, v) → F'_8
  114. Polygon(E'_8, G'_8, F'_8) → poly1', f'_8, e'_8, g'_8
  115. Translate(B, z) → E'_9
  116. Translate(A, z) → G'_9
  117. Translate(C, z) → F'_9
  118. Polygon(E'_9, G'_9, F'_9) → poly1'_1, f'_9, e'_9, g'_9
  119. Translate(B, w) → E'_{10}
  120. Translate(A, w) → G'_{10}
  121. Translate(C, w) → F'_{10}
  122. Polygon(E'_{10}, G'_{10}, F'_{10}) → poly1'_2, f'_{10}, e'_{10}, g'_{10}
  123. Translate(B, u) → E'_{11}
  124. Translate(A, u) → G'_{11}
  125. Translate(C, u) → F'_{11}
  126. Polygon(E'_{11}, G'_{11}, F'_{11}) → poly1'_3, f'_{11}, e'_{11}, g'_{11}
  127. Angle(K, A_1, D_1) → δ
  128. Angle(K, C_1, D_1) → ε
  129. Angle(D_1, B_1, M) → ζ
  130. Angle(R, G_1, E_1) → η
  131. Angle(E_1, H_1, R) → θ
  132. Angle(E_1, F_1, Q) → ι
  133. Segment(R, G_1) → j_2
  134. Segment(G_1, P) → k_2
  135. Segment(P, F_1) → l_2
  136. Segment(F_1, Q) → m_2
  137. Segment(Q, H_1) → n_2
  138. Segment(H_1, R) → p_2
  139. Segment(N, M1) → q_2
  140. Segment(M1, D) → r_2
  141. Segment(D, N1) → s_2
  142. Segment(N1, O) → t_2
  143. Segment(O, O1) → a_3
  144. Segment(O1, N) → b_3
  145. Angle(Z, T, A1) → κ
  146. Angle(A1, T, W) → λ
  147. Angle(A1, U, T) → μ
  148. Angle(S, U, A1) → ν
  149. Angle(A1, S, U) → ξ
  150. Angle(T, S, Z) → ο
  151. Line(H_1, E_1) → c
  152. Line(G_1, E_1) → c_3
  153. Line(F_1, E_1) → d_3
  154. Intersect(k_1, d_3) → E, F
  155. Intersect(k_1, c_3) → G, I_1
  156. Intersect(k_1, c) → J_1, K_1
  157. Segment(G, I_1) → e_3
  158. Segment(J_1, K_1) → f_3
  159. Segment(F, E) → g_3
  160. Circle(A, C, B) → h_3
  161. Midpoint(g_1) → L_1
  162. Midpoint(f_1) → M_1
  163. Segment(M_1, C) → i_3
  164. Segment(L_1, A) → j_3
  165. Intersect(i_3, j_3) → N_1
  166. Midpoint(C_2, N_1) → O_1
  167. Midpoint(N_1, I) → Q_1
  168. Midpoint(N_1, J) → R_1
  169. Midpoint(N_1, O_1) → T_1
  170. Midpoint(R_1, J) → U_1
  171. Midpoint(Q_1, I) → V_1
  172. Vector(T_1, O_1) → u_1
  173. Vector(Q_1, V_1) → v_1
  174. Midpoint(U_1, J) → P_1
  175. Midpoint(N_1, H) → S_1
  176. Midpoint(S_1, L_1) → W_1
  177. Midpoint(S_1, W_1) → Z_1
  178. Midpoint(S_1, Z_1) → A_2
  179. Vector(W_1, A_2) → w_1
  180. Vector(R_1, P_1) → z_1