Parallel and Perpendicular Lines Construction

GeoGebra Commands & Parameters

1. PointIn(e) → A
2. PointIn(e) → B
3. PointIn(e) → C
4. PointIn(e) → D
5. Line(A, B) → f
6. Line(C, D) → g
7. Mode(l1) → l2
8. Length(l2) → h
9. Intersect(f, g) → E
10. Angle(f, g) → α
11. If(h ≟ 0, "(1) is true", "(1) is false") → text2
12. If(α ≟ pi / 2, "(2) is true", "(2) is false") → text3
13. Point(f) → F
14. Point(g) → G
15. Slope(f) → j
16. Slope(g) → k
17. Numerator(j) → l
18. Denominator(j) → m
19. Numerator(k) → n
20. Denominator(k) → o
21. Polygon(F, (x(F) + m, y(F)), (x(F) + m, y(F) + l)) → t1, p, f_1, q
22. Segment(F, H) → r
23. Segment(H, I) → s
24. Dilate(F, If[0 < t ≤ 1, 1 - t, 0], G) → F'
25. Vector(F, F') → u
26. Translate(t1, u) → t1'
27. Translate(H, u) → H'
28. Translate(I, u) → I'
29. Segment(H', I') → s'
30. Translate(F, u) → F'_{1}
31. Translate(H, u) → H'_{1}
32. Segment(F'_{1}, H'_{1}) → r'
33. Segment(F, I) → g_1
34. Translate(F, u) → F'_{2}
35. Translate(I, u) → I'_{1}
36. Segment(F'_{2}, I'_{1}) → h_1
37. If(j ≟ k, 1, 2) → w
38. Rotate(t1', If[t > 1, (pi / 2 * (t - 1)), pi / 2], G) → t1''
39. Rotate(F'_{1}, If[t > 1, (pi / 2 * (t - 1)), pi / 2], G) → L
40. Rotate(H'_{1}, If[t > 1, (pi / 2 * (t - 1)), pi / 2], G) → M
41. Segment(L, M) → r''
42. Rotate(H', If[t > 1, (pi / 2 * (t - 1)), pi / 2], G) → H''
43. Rotate(I', If[t > 1, (pi / 2 * (t - 1)), pi / 2], G) → I''
44. Segment(H'', I'') → s''
45. Rotate(F'_{2}, If[t > 1, (pi / 2 * (t - 1)), pi / 2], G) → N
46. Rotate(I'_{1}, If[t > 1, (pi / 2 * (t - 1)), pi / 2], G) → O
47. Segment(N, O) → i_1
48. Angle(I, H, F) → β
49. Angle(I', H', F'_{1}) → γ
50. Angle(I'', M, G) → δ
51. Angle(H', G, M) → ε
52. If(Length[l2] ≟ 0, "No coordinates repeat.", "You have repeated coordinates.") → text5