Properties of a Trapezoid by Alfred Estberg

GeoGebra Commands & Parameters

1. Segment(A, B) → a
2. Line(D, a) → b
3. Point(b) → C
4. Polygon(A, B, C, D) → poly1, a_1, b_1, c, d
5. Segment(A, C) → e
6. Segment(B, D) → f
7. Mirror(B, e) → B'
8. Circle(B, (Distance[B, B'] * ReflectAC / 10)) → g
9. Intersect(g, Segment[B, B']) → E, F
10. Polygon(A, C, E) → poly2, e_1, a_2, c_1
11. Mirror(A, f) → A'
12. Circle(A, (Distance[A, A'] * ReflectBD / 10)) → h
13. Intersect(h, Segment[A, A']) → G, H
14. Polygon(B, D, G) → poly3, g_1, b_2, d_1
15. Polygon(A, C, F) → poly4, f_1, a_3, c_2
16. Intersect(e, f) → I
17. Rotate(A, α, I) → A'_1
18. Rotate(B, α, I) → B'_1
19. Rotate(C, α, I) → C'
20. Rotate(D, α, I) → D'
21. Polygon(A'_1, B'_1, C', D') → poly1', a'_1, b'_1, c', d'
22. Segment(A'_1, C') → i
23. Segment(B'_1, D') → j
24. OrthogonalLine(D, c) → k
25. OrthogonalLine(C, c) → l
26. Intersect(k, a_1) → J
27. Intersect(l, a_1) → K
28. Segment(J, K) → m
29. Intersect(((-(x(Line[D, C]) / y(Line[D, C]))) * x) - z(Line[D, C]) / y(Line[D, C]), c, 1) → O
30. OrthogonalLine(D, c) → n
31. OrthogonalLine(C, c) → p
32. Intersect(n, a_1) → L
33. Intersect(p, a_1) → M
34. Segment(L, M) → q
35. Point(Segment[L, M]) → N
36. OrthogonalLine(N, a_1) → r
37. Intersect(r, c) → P
38. Ray(A, B) → s
39. Ray(D, C) → t
40. Circle(A, ((2 * ReflectPerp) * Segment[A, N])) → h_1
41. Intersect(h_1, s) → Q, S
42. Circle(D, ((2 * ReflectPerp) * Segment[D, P])) → d_2
43. Intersect(d_2, t) → R, T
44. Polygon(P, R, Q, N) → q1, p_2, r_3, q_2, n_2
45. Polygon(P, T, S, N) → q2, p_3, t_3, s_3, n_3