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SSA Test for Similarity of Triangles

SSA Test for Similarity of Triangles
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2020-01-24 08:23
TriangleAngleGeometric Construction
This example demonstrates that the SSA (two sides and an included angle) is not a valid criterion for determining the similarity of triangles. It involves the core mathematical concept of conditions for similar triangles. Using GeoGebra commands such as Segment, Rotate, Angle, etc., different scenarios of triangles are constructed to help understand why SSA cannot be used as a criterion for triangle similarity. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Rotate(B, α, A) → B'
  3. Angle(B, A, B') → β
  4. Line(A, B') → b
  5. Point(b) → C
  6. Segment(B, C) → c
  7. Segment(C, A) → d
  8. Segment(D, E) → e
  9. Rotate(E, α, D) → E'
  10. Line(D, E') → f
  11. Angle(E, D, E') → γ
  12. Circle(D, (a * r)) → g
  13. Intersect(g, e, 1) → F
  14. Segment(D, F) → h
  15. Circle(F, (c * r)) → k
  16. Intersect(k, f, 2) → G
  17. Segment(G, F) → i
  18. Segment(G, D) → j
  19. Angle(G, F, D) → δ
  20. Angle(D, G, F) → ε
  21. Angle(C, B, A) → ζ
  22. Angle(A, C, B) → η
  23. Polygon(C, B, A) → poly1, a_1, c_1, b_1
  24. Polygon(G, F, D) → poly2, d_1, g_1, f_1

AI Drawing Prompt Reference

Draw two triangles ABC and DEF, where AB and DE are known sides and ∠BAC and ∠EDF are known included angles. Through rotation and constructing line segments, ensure that ∠BAC = ∠EDF but triangles ABC and DEF are not similar. First, draw AB and DE, then rotate B and E around A and D respectively, next draw AC and DF, and finally use circles and intersection points to construct BC and EF, ensuring that ∠BCA = ∠EFD but triangles ABC and DEF are not similar.
The prompt above was compiled from the original drawing commands and is for reference only.