Angle-Angle-Side (AAS) Triangle Congruence Dynamic Demonstration

Angle-Angle-Side (AAS) Triangle Congruence Dynamic Demonstration
几何画板及绘图内容加载中,请稍等……
2017-04-11 22:17
This GeoGebra example dynamically demonstrates the Angle-Angle-Side (AAS) condition for triangle congruence. It visually shows that if two angles and a non-included side of one triangle are equal to the corresponding parts of another triangle, the triangles are congruent. The construction uses commands such as Rotate, Angle, Ray, Point, Segment, and Polygon, with objects like text1, ABC_1, BAC, LengthAC, and variables α, β, γ for angles and a, b, c for side lengths. Users can drag vertices to see how the triangle changes while maintaining the AAS condition. This is ideal for middle school geometry lessons, high school review, or teacher demonstrations to reinforce the concept of triangle congruence.

GeoGebra 命令及参数

  1. Rotate(A, (-ABC_1), B) → B'
  2. Angle(B', B, A) → α
  3. Ray(B, B') → a
  4. Point(a) → C_1
  5. Segment(B, C_1) → b
  6. Segment(B, A) → c
  7. Angle(D_1, A, B) → β
  8. Rotate(D_1, (-(β - BAC)), A) → C
  9. Angle(C, A, D_1) → γ
  10. Segment(A, C) → d
  11. Angle(C, A, B) → δ
  12. Segment(B, C_1) → e
  13. Segment(C_1, C) → f
  14. Polygon(B, C, A) → poly1, a_1, b_1, c_1
  15. Segment(C, B) → g
  16. Segment(B, A) → h
  17. Angle(A, C, B) → ε
  18. Point(Circle[F, 12.5]) → E
  19. Segment(F, E) → i
  20. Rotate(E, 56°, F) → D
  21. Angle(E, F, D) → ζ
  22. Angle(F, D, E) → η
  23. Segment(F, D) → j
  24. Segment(D, E) → k
  25. Angle(D, E, F) → θ

AI 绘图提示语参考

绘制一个动态演示三角形全等条件(角角边)的几何图形。先构造一个三角形,其中一个顶点可拖动,通过旋转和射线构造出与给定角相等的角,并确定另一条边上的点,从而形成两个三角形。显示所有内角的角度值,并用不同颜色或标签区分对应相等的角和边。拖动顶点时,两个三角形保持对应角相等且非夹边相等,直观展示角角边判定定理。图形中包含三角形、射线、线段、角度标注和顶点标签,适合教学演示。
以上提示语为根据原始绘图命令整理而来,仅供参考。