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Two Sets of Similar Triangles

Two Sets of Similar Triangles
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2016-12-21 22:36
TriangleCirclePolygonGeometric Construction
This example demonstrates the construction and properties of two sets of similar triangles. Key math concepts include triangle similarity criteria and properties, geometric transformations, and the integration of circles and polygons. Construction highlights involve GeoGebra commands like Polygon, Rotate, Line, Intersect, Similartriangle, and Segment. Suitable for high school mathematics education to understand triangle similarity theorems and applications.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Rotate(A_1, (-Angle[C, B, A]), B_1) → D
  3. Rotate(B_1, Angle[B, A, C], A_1) → E
  4. Line(B_1, D) → f
  5. Line(A_1, E) → g
  6. Intersect(f, g) → C_1
  7. Polygon(C_1, A_1, B_1) → poly2, b_1, c_1, a_1
  8. Similartriangle(A, B, C, A_2, B_2) → poly3, C_2
  9. Polygon(F, G, H) → poly4, h, f_1, g_1
  10. Similartriangle(F, G, H, A_1, A_2) → poly5, A_3
  11. Similartriangle(F, G, H, B_1, B_2) → poly6, B_3
  12. Similartriangle(F, G, H, C_1, C_2) → poly7, C_3
  13. Polygon(A_3, B_3, C_3) → poly8, c_3, a_3, b_3
  14. Segment(A_2, B_2) → i
  15. Segment(A_2, C_2) → j
  16. Segment(C_2, B_2) → k
  17. Segment(C_1, C_3) → l
  18. Segment(C_3, C_2) → m
  19. Segment(C_2, C_1) → n
  20. Segment(A_1, A_2) → p
  21. Segment(A_2, A_3) → q
  22. Segment(A_3, A_1) → r
  23. Segment(B_1, B_3) → s
  24. Segment(B_3, B_2) → t
  25. Segment(B_2, B_1) → h_1