利用反射构造的勾股定理证明

GeoGebra 命令及参数

1. Line(A, B) → a
2. OrthogonalLine(B, a) → b
3. Point(b) → C
4. Polygon(A, B, C) → poly1, c, a_1, b_1
5. Mirror(B, b_1) → B'
6. Segment(B, B') → d
7. Intersect(b_1, d) → D
8. Mirror(D, c) → D'
9. Mirror(D, a_1) → D'_1
10. Polygon(D'_1, B, C) → poly2, c_1, d'_1, b_2
11. Polygon(B, D', A) → poly3, a_2, b_3, d'
12. Polygon(C, B', A) → poly4, a_3, c_2, b'
13. Segment(B, B + (f(t - 1) * (B' - B))) → e
14. Polygon(A, B'', C) → Triangle1, c_3, a_4, b''
15. Polygon(A, B, D_2) → Triangle2, d'', a_5, b_4
16. Polygon(B, C, D_3) → Triangle3, d'_1', b_5, c_4
17. Angle(C, D, B'') → α
18. Angle(C, B, A) → β