三角形全等条件

三角形全等条件
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2017-05-09 12:10
本范例演示了三角形全等的条件。通过构造三角形及其相关元素,如边长、角度和旋转,学生可以直观地理解全等三角形的判定定理。使用了Segment(线段)、Circle(圆)、Point(点)、Intersect(交点)、Polygon(多边形)、Angle(角)、Rotate(旋转)等GeoGebra命令。适合初中几何学习。

GeoGebra 命令及参数

  1. Segment(A_1, B_1) → a_1
  2. Circle(A_1, B_1) → circle1_1
  3. Circle(C_1, B_1) → circle1_2
  4. Segment(B_1, C_1) → b_1
  5. Segment(C_1, A_1) → c_1
  6. Point(Circle[E_1, abs(a_1)]) → D_1
  7. Circle(D_1, c_1) → circle1_3
  8. Circle(E_1, b_1) → circle1_4
  9. Intersect(circle1_3, circle1_4, 1) → F_1
  10. Segment(D_1, E_1) → d_1
  11. Segment(E_1, F_1) → e_1
  12. Segment(D_1, F_1) → f_1
  13. Polygon(A_1, B_1, C_1) → poly1_1, mc_1, ma_1, mb_1
  14. Polygon(D_1, E_1, F_1) → poly1_2, mf_1, md_1, me_1
  15. Circle(B_2, A_2) → circle2_1
  16. Circle(B_2, C_2) → circle2_2
  17. Segment(A_2, B_2) → a_2
  18. Segment(B_2, C_2) → b_2
  19. Segment(A_2, C_2) → c_2
  20. Angle(C_2, B_2, A_2) → α_21
  21. Circle(E_2, a_2) → circle2_3
  22. Circle(E_2, b_2) → circle2_4
  23. Point(circle2_3) → D_2
  24. Rotate(D_2, (-α_21), E_2) → E_2'
  25. Line(E_2, E_2') → line2'
  26. Intersect(circle2_4, line2', 2) → F_2
  27. Segment(D_2, E_2) → d_2
  28. Segment(E_2, F_2) → e_2
  29. Segment(D_2, F_2) → f_2
  30. Angle(F_2, E_2, D_2) → α_22
  31. Polygon(A_2, B_2, C_2) → poly2_1, mc_2, ma_2, mb_2
  32. Polygon(D_2, E_2, F_2) → poly2_2, mf_2, md_2, me_2
  33. Segment(B_{34}, C_{34}) → b_{34}
  34. Circle(B_{34}, C_{34}) → circle34_1
  35. Segment(B_{34}, A_{34}) → a_{34}
  36. Segment(C_{34}, A_{34}) → c_{34}
  37. Angle(C_{34}, B_{34}, A_{34}) → α_31
  38. Angle(B_{34}, C_{34}, A_{34}) → β_31
  39. Circle(E_{34}, b_{34}) → circle34_2
  40. Point(circle34_2) → F_{34}
  41. Rotate(F_{34}, α_31, E_{34}) → F_{34}'
  42. Rotate(E_{34}, (-β_31), F_{34}) → E_{34}'
  43. Line(E_{34}, F_{34}') → line34_1'
  44. Line(F_{34}, E_{34}') → line34_2'
  45. Intersect(line34_1', line34_2') → D_{34}
  46. Segment(D_{34}, E_{34}) → d_{34}
  47. Segment(E_{34}, F_{34}) → e_{34}
  48. Segment(D_{34}, F_{34}) → f_{34}
  49. Angle(F_{34}, E_{34}, D_{34}) → α_32
  50. Angle(D_{34}, F_{34}, E_{34}) → β_32
  51. Polygon(A_{34}, B_{34}, C_{34}) → poly34_1, ma_3, mb_3, mc_3
  52. Polygon(D_{34}, E_{34}, F_{34}) → poly34_2, md_3, me_3, mf_3
  53. Angle(C_{34}, A_{34}, B_{34}) → β_41
  54. Angle(F_{34}, D_{34}, E_{34}) → β_42
  55. Segment(A_5, C_5) → c_5
  56. OrthogonalLine(C_5, c_5) → line5_1'
  57. Point(line5_1') → B_5
  58. Segment(A_5, B_5) → a_5
  59. Segment(B_5, C_5) → b_5
  60. Circle(D_5, c_5) → circle5_1
  61. Point(circle5_1) → F_5
  62. Segment(D_5, F_5) → f_5
  63. OrthogonalLine(F_5, f_5) → line5_2'
  64. Circle(D_5, a_5) → circle5_2
  65. Intersect(circle5_2, line5_2', 1) → E_5
  66. Segment(D_5, E_5) → d_5
  67. Segment(E_5, F_5) → e_5
  68. Angle(A_5, C_5, B_5) → α_51
  69. Angle(D_5, F_5, E_5) → α_52
  70. Polygon(A_5, B_5, C_5) → poly5_1, mc_5, ma_5, mb_5
  71. Polygon(D_5, E_5, F_5) → poly5_2, mf_5, md_5, me_5
  72. Segment(A_6, B_6) → a_6
  73. Circle(B_6, A_6) → circle6_1
  74. Circle(A_6, C_6) → circle6_2
  75. Segment(B_6, C_6) → b_6
  76. Segment(A_6, C_6) → c_6
  77. Circle(D_6, a_6) → circle6_3
  78. Point(circle6_3) → E_6
  79. Circle(D_6, c_6) → circle6_4
  80. Angle(C_6, B_6, A_6) → α_61
  81. Rotate(D_6, (-α_61), E_6) → F_6'
  82. Line(E_6, F_6') → line6'
  83. Intersect(circle6_4, line6', 1) → F_6
  84. Segment(D_6, E_6) → d_6
  85. Segment(E_6, F_6) → e_6
  86. Segment(D_6, F_6) → f_6
  87. Angle(F_6, E_6, D_6) → α_62
  88. Polygon(A_6, B_6, C_6) → poly6_1, mc_6, ma_6, mb_6
  89. Polygon(D_6, E_6, F_6) → poly6_2, mf_6, md_6, me_6
  90. Segment(A_7, B_7) → a_7
  91. Segment(B_7, C_7) → b_7
  92. Segment(A_7, C_7) → c_7
  93. Segment(D_7, E_7) → d_7
  94. Angle(C_7, A_7, B_7) → α_71
  95. Angle(A_7, B_7, C_7) → β_71
  96. Angle(B_7, C_7, A_7) → γ_71
  97. Rotate(E_7, (-α_71), D_7) → F_71'
  98. Rotate(D_7, β_71, E_7) → F_72'
  99. Line(D_7, F_71') → line7_1'
  100. Line(E_7, F_72') → line7_2'
  101. Intersect(line7_1', line7_2') → F_7
  102. Segment(D_7, F_7) → e_7
  103. Segment(E_7, F_7) → f_7
  104. Angle(F_7, D_7, E_7) → α_72
  105. Angle(D_7, E_7, F_7) → β_72
  106. Angle(E_7, F_7, D_7) → γ_72
  107. Polygon(A_7, B_7, C_7) → poly7_1, mc_7, ma_7, mb_7
  108. Polygon(D_7, E_7, F_7) → poly7_2, mf_7, md_7, me_7

AI 绘图提示语参考

画两个三角形,分别标记三个顶点和三条边,用圆表示边长,用角度符号表示三个内角,通过旋转和相交操作展示三角形全等的条件,包括边边边、边角边和角边角三种情况,并用不同颜色区分两个三角形,以便观察全等关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。