垂直直线的快速发现：用几何作图求交与夹角

GeoGebra 命令及参数

1. Line(A, B) → f
2. Slope(f) → a
3. Denominator(a) → run
4. Numerator(a) → rise
5. OrthogonalLine(C, f) → g
6. Intersect(f, g) → D
7. Angle(B, D, C) → α
8. Intersect(h, i) → E
9. Polygon(A, E, B) → t1, b, a_1, e
10. Segment(A, E) → j
11. Segment(E, B) → k
12. Segment(B, A) → l
13. Distance(C, F) → distanceCF
14. Distance(B, E) → distanceBE
15. Intersect(g, n) → G
16. Dilate(A, If[0 < c ≤ 1, 1 - c, 0], G) → A'
17. Vector(A, A') → u
18. Translate(A, u) → A'_1
19. Translate(E, u) → E'
20. Translate(B, u) → B'
21. Polygon(A'_1, E', B') → t1', b', a'_1, e'
22. Segment(A'_1, E') → p
23. Segment(E', B') → q
24. Segment(B', A'_1) → r
25. Angle(B', E', A'_1) → β
26. Angle(B, E, A) → γ
27. Rotate(A'_1, If[1 < c ≤ 2, ((c - 1) * π / 2), π / 2], G) → H
28. Rotate(E', If[1 < c ≤ 2, ((c - 1) * π / 2), π / 2], G) → E''
29. Rotate(B', If[1 < c ≤ 2, ((c - 1) * π / 2), π / 2], G) → B''
30. Polygon(H, E'', B'') → t1'', b'', h_1, e''
31. Segment(G, E'') → s
32. Segment(E'', B'') → t
33. Segment(B'', G) → d
34. Angle(B'', E'', G) → δ