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Triangle Construction under SSS Condition

Triangle Construction under SSS Condition
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2017-02-01 07:29
TrianglePolygonGeometric Construction
This example demonstrates how to construct a triangle under the SSS (Side-Side-Side) condition. The core mathematical concepts involved include geometric construction and triangle congruence theorems. Key construction steps use GeoGebra commands and objects such as Segment, Line, Circle, Intersect, Polygon, and Mirror. Suitable for middle school students and above learning geometric constructions and triangle properties.

GeoGebra Commands & Parameters

  1. Segment(A, B) → c
  2. Segment(B, C) → a
  3. Segment(C, A) → b
  4. Line(D_1, E_1) → d_1
  5. Circle(E_1, c) → e_2
  6. Intersect(e_2, d_1, 1) → F_1
  7. Segment(F_1, E_1) → f_2
  8. Circle(E_1, a) → g
  9. Circle(F_1, b) → h
  10. Intersect(g, h, 2) → G
  11. Segment(F_1, G) → i
  12. Segment(G, E_1) → j
  13. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  14. Polygon(F_1, E_1, G) → poly2, g_1, f_1, e_1
  15. Line((2, 0), (12, 16)) → l
  16. Mirror(F_1, l) → D
  17. Mirror(E_1, l) → E
  18. Mirror(G, l) → F
  19. Polygon(D, E, F) → poly2', g', f', e'
  20. Mirror(F_1, l) → F'_1
  21. Mirror(E_1, l) → E'_1
  22. Segment(F'_1, E'_1) → f
  23. Mirror(G, l) → G'_1
  24. Mirror(E_1, l) → E'_2
  25. Segment(G'_1, E'_2) → d
  26. Mirror(F_1, l) → F'_2
  27. Mirror(G, l) → G'_2
  28. Segment(F'_2, G'_2) → e