Discovering the SAS Similarity Theorem

GeoGebra Commands & Parameters

1. Segment(A, B) → a
2. Segment(B, C) → b_2
3. Segment(C, A) → b
4. Vector(A, D) → u
5. Dilate(A, k, A) → A'
6. Dilate(B, k, A) → B'
7. Segment(A', B') → a'_2
8. Dilate(C, k, A) → C'
9. Dilate(A, k, A) → A'_1
10. Segment(C', A'_1) → c'
11. Dilate(B, k, A) → B'_1
12. Dilate(C, k, A) → C'_1
13. Segment(B'_1, C'_1) → b'_2
14. Polygon(A'_1, B'_1, C'_1) → poly1, c'_1, a'_1, b'_1
15. Dilate(A, m, D) → A'_2
16. Vector(A, A'_2) → v
17. Translate(A'_1, v) → E
18. Translate(B'_1, v) → F
19. Translate(C'_1, v) → G
20. Polygon(E, F, G) → poly1', g, e, f
21. Polygon(A, C, B) → poly2, b_1, a_1, c_1
22. Segment(F, A'_2) → a'
23. Segment(A'_2, G) → b'
24. Segment(G, F) → i
25. Angle(B, A, C) → α
26. Vector(D, A) → w
27. Circle(A, 0.5) → p
28. Intersect(p, a) → H,
29. Intersect(p, b) → I,
30. Circle(A'_2, 0.5) → q
31. Intersect(q, a', 1) → J
32. Intersect(q, b', 1) → K
33. CircleSector(A'_2, J, K) → r
34. CircleSector(A, H, I) → s
35. Angle(H, A, I) → β
36. CircleSector(A, I, H) → t
37. CircleSector(A'_2, K, J) → d_1
38. Circle(B, 0.5) → c
39. Circle(F, 0.5) → d
40. Intersect(c, b_2, 1) → L
41. Intersect(c, a, 1) → M
42. Intersect(d, i, 1) → N
43. Intersect(d, a', 1) → O
44. CircleSector(F, N, O) → h
45. CircleSector(B, L, M) → e_1
46. CircleSector(F, O, N) → f_1
47. Dilate(F, 1 - j, B) → F'
48. Vector(F, F') → l
49. Translate(h, l) → h'
50. Translate(f_1, l) → g_1
51. Textfield(k) → InputBox1