How the Orthocenter Cuts the Altitude in a Right Triangle

GeoGebra Commands & Parameters

1. Line(A, B) → a
2. Line(B, C) → b
3. Line(C, A) → c
4. OrthogonalLine(C, a) → d
5. OrthogonalLine(A, b) → e
6. OrthogonalLine(B, c) → f
7. Intersect(d, e) → D
8. Intersect(a, d) → E
9. Segment(D, E) → g
10. Segment(D, C) → h
11. Intersect(b, e) → F
12. Segment(F, D) → i
13. Segment(D, A) → j
14. Segment(B, D) → k
15. Intersect(c, f) → G
16. Segment(D, G) → l
17. Segment(A, B) → m
18. Segment(B, C) → n
19. Segment(A, C) → p
20. Segment(C, B) → q
21. Rotate(F, 90°, D) → F'
22. Rotate(D, 90°, D) → D'
23. Segment(F', D') → i'
24. Rotate(D, 90°, D) → D'_1
25. Rotate(E, 90°, D) → E'
26. Segment(D'_1, E') → g'
27. Rotate(D, 90°, D) → D'_2
28. Rotate(G, 90°, D) → G'
29. Segment(D'_2, G') → l'
30. OrthogonalLine(E', g') → r
31. OrthogonalLine(C, h) → s
32. Intersect(r, s) → H
33. Polygon(E', D, C, H) → poly1, e', d_1, c_1, h_1
34. OrthogonalLine(A, j) → t
35. OrthogonalLine(F', i') → a_1
36. Intersect(t, a_1) → I
37. Polygon(F', D, A, I) → poly2, f', d_2, a_2, i_1
38. OrthogonalLine(B, k) → b_1
39. OrthogonalLine(G', l') → e_1
40. Intersect(b_1, e_1) → J
41. Polygon(D, B, J, G') → poly3, d_3, b_2, j_1, g'_1
42. PointIn(poly2) → Pointpoly2
43. PointIn(poly3) → Pointpoly3
44. PointIn(poly1) → Pointpoly1