几何平均数构造演示：直角三角形与垂线定理展示几何平均数的几何意义

GeoGebra 命令及参数

1. Segment(A, B) → AB
2. OrthogonalLine(A, AB) → g
3. Point(g) → C
4. Segment(C, B) → BC
5. Segment(C, A) → AC
6. Segment(A, B) → j
7. Angle(B, A, C) → α
8. OrthogonalLine(A, BC) → k
9. Intersect(k, BC) → D
10. Angle(C, D, A) → β
11. Segment(A, D) → AD
12. Segment(B, D) → BD
13. Point(Circle[a, AC]) → c
14. Segment(a, c) → ac
15. Point(Circle[a, AB]) → b
16. Segment(a, b) → ab
17. Angle(b, a, c) → γ
18. Segment(c, b) → bc
19. Point(Circle[a'', AD]) → d''
20. Segment(a'', d'') → a''d''
21. Point(Circle[d'', BD]) → b'
22. Segment(d'', b') → b'd''
23. Segment(a'', b') → a''b'
24. Angle(b', d'', a'') → ε
25. Polygon(c, a, b) → poly1, b_2, c_2, a_2
26. Polygon(a'', d'', b') → poly3, b'_1, a''_1, d''_1
27. Angle(a, c, b) → ζ
28. Angle(d'', a'', b') → θ
29. Point(Circle[d', Distance[C, D]]) → c'
30. Segment(d', c') → c'd'
31. Point(Circle[d', AD]) → a'
32. Segment(d', a') → a'd'
33. Angle(a', d', c') → δ
34. Segment(c', a') → a'c'
35. Angle(d', c', a') → η
36. Polygon(c', d', a') → poly2, a'_1, c'_1, d'_1