Complementary Angles Investigation

GeoGebra Commands & Parameters

1. Circle(A, B) → c
2. Segment(A, B) → a
3. Point(b) → C
4. Ray(A, C) → d
5. Point(d) → D
6. Circle(D, a) → e
7. Midpoint(A, D) → E
8. OrthogonalLine(E, b) → f
9. Point(f) → F
10. Ray(E, F) → g
11. Point(g) → G
12. Intersect(c, b) → H, I
13. Intersect(e, b) → J, K
14. Rotate(I, α, A) → I'
15. Angle(I, A, I') → β
16. Rotate(K, π / 2 - β, D) → K'
17. Angle(K, D, K') → γ
18. Circle(A, (0.4 * a)) → h
19. Circle(D, (0.4 * a)) → k
20. Segment(A, I') → i
21. Segment(D, K') → j
22. Intersect(h, b, 2) → L
23. Intersect(h, i, 1) → M
24. Intersect(k, b, 2) → N
25. Intersect(k, j, 1) → O
26. Circle(G, a) → p
27. Intersect(p, l, 2) → P
28. Intersect(p, l, 1) → Q
29. Intersect(p, g, 1) → R
30. Vector(G, P) → u
31. Vector(G, R) → v
32. CircleSector(A, L, M) → q
33. CircleSector(D, N, O) → r
34. Dilate(A, If[0 < m ≤ 1, 1 - m, 0], G) → A'
35. Vector(A, A') → w
36. Translate(q, w) → q'
37. Rotate(q', If[1 < m ≤ 2, ((m - 1) * (π / 2 - α)), π / 2 - α], G) → q''
38. Dilate(D, If[2 < m ≤ 3, 3 - m, 0], G) → D'
39. Vector(D, D') → n
40. Translate(r, n) → r'
41. Vector(G, Q) → s
42. Angle(R, G, Q) → δ
43. Vector(A, I') → u_1
44. Vector(A, I) → t
45. Vector(D, K) → v_1
46. Vector(D, K') → w_1