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Proving Triangles Similar with Transformations

Proving Triangles Similar with Transformations
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2017-03-24 05:27
TriangleTransformationGeometric Construction
In collections Proving Figures Similar
This example demonstrates proving triangles similar using geometric transformations. It covers concepts such as translation, rotation, reflection, and dilation. By constructing geometric objects like rays, angles, points, segments, and polygons, the transformation process is illustrated. Suitable for middle school and above students to learn about the properties of similar triangles.

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