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SSA and Triangle Congruence

SSA and Triangle Congruence
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2019-09-27 23:56
TriangleAngleGeometric Construction
In collections Exploring Triangle Congruence
This applet dynamically demonstrates why SSA is not a valid criterion for triangle congruence. Key mathematical concepts include triangle congruence criteria. Using GeoGebra commands such as Polygon, Point, Angle, Circle, Segment, Intersect, students can observe the construction of triangles under different SSA conditions. Suitable for middle school and above students studying triangle congruence.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Point(b) → G
  3. Point(a) → H
  4. Angle(A, B, C) → γ
  5. Angle(B, C, A) → δ
  6. Angle(C, A, B) → ε
  7. Circle(B', Segment[A, B]) → d
  8. Point(d) → A'
  9. Circle(B', Segment[C, B]) → e
  10. Point(e) → C'
  11. Segment(B', C') → f
  12. Segment(B', A') → g
  13. Intersect(d, f, 1) → I
  14. CircleArc(B', A', I) → h
  15. Circle(C', Segment[H, C]) → k
  16. Circle(C', Segment[G, C]) → p
  17. Intersect(k, f, 1) → D
  18. Circle(D, Segment[H, G]) → q
  19. Intersect(p, q, 1) → E
  20. Ray(C', E) → i
  21. Point(i) → F
  22. Segment(F, C') → j
  23. Angle(A', B', C') → β
  24. Angle(B', C', F) → ζ
  25. Angle(C', F, B') → η

AI Drawing Prompt Reference

Draw triangle ABC, then mark points G and H on sides AB and AC respectively. Draw a circle through point A and point B, and another circle through point A and point C. Let the intersection points of these circles be A' and C'. Connect A'C' and B'C', and mark point I on B'C'. Draw an arc with center A' and radius A'I, intersecting B'C' at point D. Draw a circle with center D and radius DH, and let it intersect the circle with center C' and radius CG at point E. Draw a ray from C' to E, and mark the intersection point of the ray with B'C' as F. Connect F and C' to form triangle BCF.
The prompt above was compiled from the original drawing commands and is for reference only.