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Triangle Similarity Shortcuts

Triangle Similarity Shortcuts
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2016-02-26 21:44
TriangleAngleGeometric Construction
This example demonstrates shortcuts for identifying similar triangles. Key mathematical concepts include the properties and theorems of similar triangles. Using GeoGebra commands such as Segment, Rotate, Angle, and Line, two similar triangles are constructed and their corresponding sides and angles are observed. Suitable for middle and high school students learning about similar triangles.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Rotate(B, α, A) → B'
  3. Angle(B, A, B') → γ
  4. Line(A, B') → b
  5. Rotate(A, (-β), B) → A'
  6. Angle(A', B, A) → δ
  7. Line(A', B) → c
  8. Intersect(b, c) → C
  9. Polygon(A, B, C) → Tri_1, c_1, a_1, b_1
  10. Segment(D, E) → d
  11. Rotate(E, α, D) → E'
  12. Angle(E, D, E') → ε
  13. Line(E', D) → e
  14. Rotate(D, (-β), E) → D'
  15. Angle(D', E, D) → ζ
  16. Line(D', E) → f
  17. Intersect(e, f) → F
  18. Polygon(F, E, D) → Tri_2, d_1, f_1, e_1
  19. Segment(A, C) → h
  20. Segment(B, C) → i
  21. Segment(D, F) → j
  22. Segment(F, E) → k
  23. Angle(D, F, E) → η
  24. Angle(A, C, B) → θ
  25. Segment(E, F) → m
  26. Segment(F, D) → n
  27. Segment(B, C) → p
  28. Segment(C, A) → q