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Discovering the SAS Similarity Theorem by Tim Brzezinski

Discovering the SAS Similarity Theorem by Tim Brzezinski
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2016-03-26 03:11
TriangleAngleGeometric ConstructionSlider Animation
In collections Similarity & Right Triangle Trigonometry Similarity, Right Triangles, and Trigonometry (SRT) Cluster Similarity Theorems! Similar Triangles Review U9 Dilations and Similar Triangles Similar Triangles Theorem
This applet allows students to conceptually and interactively explore and discover the SAS Similarity Theorem for triangles. It involves core math concepts like triangle similarity, angle equality, side ratios, and geometric transformations. Constructed using GeoGebra commands and objects such as Segment, Vector, Dilate, Polygon, Translate, Angle, Circle, Intersect, CircleSector, and Textfield. Ideal for high school mathematics education to enhance geometric intuition and understanding of similarity theorems.

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