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Proving Triangles Similar (3)

Proving Triangles Similar (3)
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2018-10-27 12:16
TriangleAngleGeometric Construction
In collections Similar Triangles Book APS 10/27/18
This example demonstrates how to prove triangle similarity using angle relationships and side ratios. Core math concepts include triangle similarity theorems, angle equality, and side proportionality. Construction highlights involve GeoGebra commands like Ray, Rotate, Angle, Point, Segment, Polygon, Vector, Translate, and Dilate. Suitable for high school geometry instruction and construction practice.

GeoGebra Commands & Parameters

  1. Ray(D, E) → f_2
  2. Rotate(E, (a_3 * 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_2, a_1, b_2
  9. Segment(D, F) → e
  10. Angle(F, E, D) → β
  11. Vector(D_1, E_1) → u
  12. Polygon(D, E, F) → poly2, c_1, a_2, b_1
  13. Translate(D, u) → A'
  14. Translate(E, u) → B'_1
  15. Translate(F, u) → C'
  16. Polygon(A', B'_1, C') → poly2', c', a', b'_1
  17. Dilate(A', d_1, A') → A''
  18. Dilate(B'_1, d_1, A') → F_1
  19. Dilate(C', d_1, A') → C
  20. Polygon(A'', F_1, C) → poly2'', c'', a'', f_1
  21. Segment(A', C) → k
  22. Segment(C, F_1) → l
  23. Segment(F_1, A') → m
  24. Rotate(A'', (e_1 * π / 180), C) → A'''
  25. Rotate(F_1, (e_1 * π / 180), C) → B
  26. Rotate(C, (e_1 * π / 180), C) → C'''
  27. Polygon(A''', B, C''') → poly2''', c''', a_4, f'
  28. Rotate(A', (e_1 * π / 180), C) → A
  29. Segment(A, B) → c
  30. Segment(B, C) → a
  31. Segment(C, A) → b