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Similar Triangles by Gerrit Stols

Similar Triangles by Gerrit Stols
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2015-11-13 08:43
TriangleCoordinate GeometryGeometric Construction
This example demonstrates the properties and criteria of similar triangles. It involves core mathematical concepts like triangle similarity, geometric transformations, and coordinate geometry. Construction highlights include using commands like Segment, Ray, Point, Circle, Intersect, Distance, Angle, and applying transformations such as Translation and Normal Distribution. Suitable for high school mathematics education to understand applications and proofs of similar triangles.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Ray(K, D_1) → b
  3. Point(a) → F_1
  4. Circle(A, F_1) → e
  5. Segment(A, F_1) → f
  6. Circle(B, f) → g
  7. Circle(K, f) → h
  8. Segment(A, B) → i
  9. Intersect(g, i, 1) → I
  10. Distance(A, B) → distanceAB
  11. Segment(B, C) → n
  12. Intersect(g, a, 1) → G
  13. Intersect(g, n, 1) → M_1
  14. Segment(G, M_1) → r
  15. Angle(C, B, A) → β
  16. Distance(B, C) → distanceBF
  17. Segment(K, L) → c
  18. Point(g) → F
  19. Segment(B, F) → d
  20. Circle(L, d) → k
  21. Intersect(h, c, 1) → J
  22. Intersect(k, c, 1) → L_1
  23. Circle(L_1, r) → q
  24. Intersect(k, q, 2) → N_1
  25. Ray(L, N_1) → t
  26. Distance(L, K) → distanceLK
  27. Segment(A, C) → k_1
  28. Angle(B, A, C) → ι
  29. Angle(A, C, B) → κ
  30. Distance(A, C) → distanceAC
  31. Intersect(k, q, 2) → D
  32. Ray(L, D) → j
  33. Intersect(e, k_1) → H,
  34. Intersect(h, c) → M,
  35. Intersect(a, i) → E
  36. Intersect(a, i) → N
  37. Intersect(a, i) → O
  38. Intersect(e, a) → P,
  39. Segment(P, H) → l
  40. Circle(M, l) → p
  41. Intersect(h, p, 1) → Q
  42. Ray(K, Q) → m
  43. Intersect(m, j) → R
  44. Angle(L, K, R) → α
  45. Angle(K, R, L) → γ
  46. Angle(R, L, K) → δ
  47. Angle(r, k_1) → ε
  48. Segment(K, R) → s
  49. Segment(L, R) → a_1
  50. Distance(K, R) → distanceKR
  51. Distance(L, R) → distanceLR