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Proving Triangles Similar (4)

Proving Triangles Similar (4)
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2018-10-27 12:18
TriangleTransformationGeometric Construction
In collections Similar Triangles Book APS 10/27/18
This example demonstrates how to prove triangle similarity through construction and transformation; involves core concepts like triangle similarity criteria, geometric transformations, and vector operations; constructed using GeoGebra commands such as Ray, Rotate, Angle, Point, Segment, Polygon, Line, Intersect, Mirror, and Dilate; suitable for high school mathematics teaching and geometric transformation learning.

GeoGebra Commands & Parameters

  1. Ray(D, E) → f_2
  2. Rotate(E, (a_2 * π / 180), D) → B'
  3. Angle(E, D, B') → α
  4. Ray(D, B') → g
  5. Point(g) → F
  6. Segment(F, E) → d
  7. Segment(D, E) → f
  8. Polygon(D, E, F) → poly1, c_1, a_1, b_1
  9. Segment(D, F) → e
  10. Angle(F, E, D) → β
  11. Point(e) → D_1
  12. Line(D_1, d) → k
  13. Intersect(k, f) → E_1
  14. Line(I, J) → n
  15. Mirror(E_1, n) → E'
  16. Mirror(D_1, n) → D'
  17. Mirror(D, n) → A'
  18. Mirror(E, n) → B'_1
  19. Mirror(F, n) → C'
  20. Polygon(A', B'_1, C') → poly1', c', a', b'_1
  21. Rotate(A', (m * π / 180), A') → A
  22. Rotate(B'_1, (m * π / 180), A') → F_1
  23. Rotate(C', (m * π / 180), A') → C''
  24. Polygon(A, F_1, C'') → poly1'', c'', a'', f_1
  25. Dilate(A, d_1, A) → A'''
  26. Dilate(F_1, d_1, A) → B
  27. Dilate(C'', d_1, A) → C
  28. Polygon(A''', B, C) → poly1''', c''', a''', f'
  29. Segment(A, C) → b
  30. Segment(A, B) → c
  31. Segment(B, C) → a