Geometric Mean Leg Theorem Demo

GeoGebra Commands & Parameters

1. Point(f) → A
2. Line(A, B) → g
3. OrthogonalLine(B, g) → h
4. Intersect(f, h) → C
5. OrthogonalLine(B, f) → i
6. Intersect(f, i) → D
7. Segment(A, B) → j
8. Segment(B, C) → b
9. Segment(C, D) → d
10. Segment(D, A) → m
11. Segment(D, B) → n
12. Angle(C, D, B) → α
13. Angle(A, B, C) → β
14. Segment(A, C) → p
15. Point(Circle[E, p]) → F
16. Segment(E, F) → c
17. Dilate(D, If[0 ≤ a < 1, 1 - a, 0], G) → G'
18. Vector(D, G') → v
19. Polygon(D, B, C) → t1, c_1, d_1, b_1
20. Translate(D, v) → D'
21. Translate(B, v) → B'
22. Translate(C, v) → C'
23. Polygon(D', B', C') → t1', c', d', b'
24. Dilate(B, If[1 ≤ a < 2, 2 - a, 0], H) → H'
25. Vector(B, H') → u
26. Polygon(B, C, A) → t2, a_1, b_2, c_2
27. Translate(B, u) → B'_1
28. Translate(C, u) → C'_1
29. Translate(A, u) → A'
30. Polygon(B'_1, C'_1, A') → t2', a', b'_1, c'_1
31. Line(B, m) → k
32. Point(k) → I
33. Angle(C, B, I) → γ
34. Rotate(B'_1, If[2 ≤ a < 3, ((a - 2) * γ), γ], H) → J
35. Rotate(C'_1, If[2 ≤ a < 3, ((a - 2) * γ), γ], H) → K
36. Rotate(A', If[2 ≤ a < 3, ((a - 2) * γ), γ], H) → A''
37. Polygon(J, K, A'') → t2'', a'', j_1, k_1
38. Line(H, K) → l
39. Mirror(J, l) → J'
40. Mirror(K, l) → K'
41. Mirror(A'', l) → A'''
42. Polygon(J', K', A''') → t2''', a''', j', k'
43. Angle(C', D', B') → δ
44. Angle(A', B'_1, C'_1) → ε
45. Angle(A'', B'_1, K) → ζ
46. Angle(K', B'_1, A''') → η
47. Angle(C', D', B') → θ