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SAS Similarity Theorem Discovery

SAS Similarity Theorem Discovery
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2016-11-29 08:32
TriangleAngleTransformationGeometric ConstructionSlider Animation
This applet allows students to conceptually and meaningfully discover the SAS Similarity Theorem for Triangles through interactive exploration. It involves core math concepts like triangle similarity criteria, angle equality, and side proportionality. Constructed using GeoGebra commands/objects such as Segment, Vector, Dilate, Polygon, Translate, Angle, Circle, Intersect, CircleSector, and Textfield. Ideal for high school mathematics students and teachers for instructional demonstration and concept validation.

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) → ka
  23. Segment(A'_2, G) → kb
  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, ka, 1) → J
  32. Intersect(q, kb, 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, ka, 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