Ratio of Areas of Similar Triangles

GeoGebra Commands & Parameters

1. Segment(B, C) → a
2. Segment(Q, R) → b
3. Rotate(B, (-α), C) → A'
4. Angle(A', C, B) → β_1
5. Rotate(C, β, B) → B'
6. Angle(C, B, B') → γ
7. Ray(B, B') → c
8. Ray(C, A') → d_1
9. Intersect(c, d_1) → A
10. Segment(A, B) → e
11. Segment(A, C) → f
12. Rotate(R, β, Q) → D_1
13. Angle(R, Q, D_1) → δ
14. Rotate(Q, (-α), R) → E_1
15. Angle(E_1, R, Q) → ε
16. Ray(Q, D_1) → g
17. Ray(R, E_1) → h
18. Intersect(g, h) → P
19. Segment(Q, P) → i
20. Segment(P, R) → j
21. Distance(B, C) → distanceAB
22. Distance(C, A) → distanceBC
23. Distance(A, B) → distanceCA
24. Distance(Q, R) → distanceA1B1
25. Distance(R, P) → distanceB1F
26. Distance(P, Q) → distanceFA1
27. Polygon(C, A, B) → poly1, a_1, b_1, c_1
28. Polygon(P, Q, R) → poly2, b_2, c_2, a_2
29. Angle(Q, P, R) → ζ
30. Angle(B, A, C) → η
31. Point(a) → M
32. Segment(A, M) → d
33. Point(b) → N
34. Segment(P, N) → k