梯形面积的几何推导与构造

GeoGebra 命令及参数

1. Segment(A, B) → a
2. Line(C, a) → b
3. Point(b) → D
4. Polygon(A, B, D, C) → poly1, a_1, b_1, d, c
5. Midpoint(c) → E
6. Midpoint(b_1) → F
7. Polygon(A, B, F, E) → poly2, a_2, b_2, f, e
8. OrthogonalLine(C, f) → g
9. Intersect(g, f) → G
10. Polygon(E, G, C) → poly3, c_1, e_1, g_1
11. Polygon(G, F, D, C) → poly4, g_2, f_1, d_1, c_2
12. Rotate(E, α, E) → E'
13. Rotate(G, α, E) → G'
14. Rotate(C, α, E) → C'
15. Polygon(E', G', C') → poly3', c', e', g'
16. Rotate(G, (-β), F) → G'_1
17. Rotate(F, (-β), F) → F'
18. Rotate(D, (-β), F) → D'
19. Rotate(C, (-β), F) → C'_1
20. Polygon(G'_1, F', D', C'_1) → poly4', g'_1, f', d', c'_1
21. Segment(E, C) → k
22. Segment(C, D) → l
23. Segment(D, F) → m