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Similar triangles on sides of a quadrilateral

Similar triangles on sides of a quadrilateral
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2017-03-13 23:05
TrianglePolygonAngleGeometric Construction
This example demonstrates constructing similar triangles on the sides of a quadrilateral. It involves core mathematical concepts like triangle similarity criteria, angle relationships, and geometric transformations. The construction uses commands and objects such as Segment, Rotate, Ray, Intersect, Polygon, and Angle in GeoGebra. Suitable for high school mathematics teaching or exploration by geometry enthusiasts.

GeoGebra Commands & Parameters

  1. Segment(C, B) → f
  2. Segment(B, A) → g
  3. Segment(A, D) → h
  4. Segment(D, C) → i
  5. Segment(C, Q) → j
  6. Segment(Q, B) → k
  7. Rotate(D, (-Angle[Q, C, B]), A) → D'
  8. Rotate(A, Angle[C, B, Q], D) → C'
  9. Ray(A, D') → l
  10. Ray(D, C') → m
  11. Intersect(l, m) → S
  12. Segment(D, S) → n
  13. Segment(A, S) → p
  14. Rotate(C, Angle[C, B, Q], D) → C'_1
  15. Rotate(D, (-Angle[Q, C, B]), C) → D'_1
  16. Ray(C, D'_1) → q
  17. Ray(D, C'_1) → r
  18. Intersect(q, r) → R
  19. Segment(C, R) → s
  20. Segment(R, D) → t
  21. Rotate(B, (-Angle[R, C, D]), A) → B'
  22. Ray(A, B') → a
  23. Rotate(A, Angle[C, D, R], B) → A'
  24. Ray(B, A') → b
  25. Intersect(a, b) → P
  26. Segment(B, P) → c
  27. Segment(P, A) → d
  28. Polygon(Q, P, S, R) → poly1, q_1, p_1, s_1, r_1
  29. Angle(S, A, D) → α
  30. Angle(R, C, D) → β
  31. Angle(P, A, B) → γ
  32. Angle(Q, C, B) → δ
  33. Angle(C, B, Q) → ε
  34. Angle(C, D, R) → ζ
  35. Angle(A, B, P) → η
  36. Angle(A, D, S) → θ