Parallelogram Theorems Quick Check

GeoGebra Commands & Parameters

1. Rotate(B, a°, A) → B'
2. Angle(B, A, B') → α
3. Ray(A, B) → f
4. Ray(A, B') → g
5. Line(B, g) → h
6. Point(g) → C
7. Line(C, f) → i
8. Intersect(h, i) → D
9. Segment(C, D) → j
10. Segment(A, B) → k
11. Segment(B, D) → l
12. Segment(A, C) → m
13. Min(m, k) → b
14. Circle(C, (0.2 * b)) → d
15. Circle(A, (0.2 * b)) → e
16. Circle(B, (0.2 * b)) → p
17. Circle(D, (0.2 * b)) → c
18. Intersect(e, k, 1) → E
19. Intersect(e, m, 1) → F
20. Intersect(p, k, 1) → G
21. Intersect(p, l, 1) → H
22. Intersect(d, g, 2) → I
23. Ray(C, I) → q
24. Intersect(c, h, 2) → J
25. Ray(D, J) → r
26. Intersect(c, i, 2) → K
27. Ray(D, K) → s
28. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'
29. Segment(A, A') → t
30. Rotate(E, If[1 < o ≤ 2, ((o - 1) * α), α], A) → E'
31. CircleSector(A, E, E') → c_1
32. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], C) → A'_1
33. Vector(A, A'_1) → u
34. Translate(c_1, u) → d_1
35. Segment(A, A'_1) → f_1
36. Dilate(C, If[3 < o ≤ 4, 4 - o, 0], D) → C'
37. Vector(C, C') → v
38. Translate(d_1, v) → e_1
39. Segment(C, C') → g_1
40. Dilate(D, If[4 < o ≤ 5, 5 - o, 0], B) → D'
41. Segment(D, D') → h_1
42. Polygon(A, B, D, C) → poly1, a_1, b_1, d_2, c_2
43. Dilate(A, If[5.5 < o ≤ 6.5, 6.5 - o, 0], C) → A'_2
44. Vector(A, A'_2) → w
45. Translate(A, w) → A'_3
46. Translate(A', w) → A''
47. Segment(A'_3, A'') → t'
48. Dilate(A, If[6.5 < o ≤ 7.5, 7.5 - o, 0], B) → A'_4
49. Vector(A, A'_4) → u_1
50. Translate(A, u_1) → A'_5
51. Translate(A'_1, u_1) → L
52. Segment(A'_5, L) → i_1