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SAS Similarity Theorem Exploration by Kevin Agnew

SAS Similarity Theorem Exploration by Kevin Agnew
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2019-02-22 21:34
TriangleTransformationGeometric Construction
This GeoGebra applet dynamically demonstrates the SAS Similarity Theorem for triangles. Key mathematical concepts include similar triangles and triangle geometry. Using commands like Segment, Vector, Dilate, and Polygon, students can visually explore the properties of similar triangles. Suitable for middle school and above students to learn about similar triangles.

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