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Triangle Properties Explorer

Triangle Properties Explorer
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2020-03-07 04:59
TriangleCircleAngleInequalityGeometric Construction
① This interactive GeoGebra applet dynamically explores various properties of triangles, including medians, centroid, circumcircle, and perpendicular lines. ② Core mathematical concepts include triangle medians and centroid (barycenter), perpendicular bisectors and circumcircle, angle-side relationships, and inequalities related to sine and random variables in a geometric context. ③ Construction highlights: based on the summary, the applet uses GeoGebra commands such as Line, Segment, Midpoint, Intersect, OrthogonalLine, Circle, Polygon, Angle, Vector, and Translate, creating vertices A, B, C, three medians (median1, median2, median3), their intersection centroid, and buttons to toggle visibility of medians, perpendiculars, circumcircle, and other objects, along with text labels. ④ Suitable for middle/high school geometry lessons, math lab activities, or self-study, helping students intuitively grasp theorems like concurrency of medians, centroid properties, circumcenter location, and perpendicular relationships.

GeoGebra Commands & Parameters

  1. Line(B, A) → f
  2. Line(A, C) → g
  3. Line(C, B) → h
  4. Segment(B, A) → i
  5. Segment(A, C) → j
  6. Segment(C, B) → k
  7. Midpoint(i) → D
  8. Midpoint(j) → E
  9. Midpoint(k) → F
  10. Segment(A, F) → median1
  11. Segment(E, B) → median3
  12. Segment(D, C) → median2
  13. Intersect(median1, median3) → centroid
  14. OrthogonalLine(F, k) → l
  15. Circle(B, A, C) → c
  16. OrthogonalLine(D, i) → m
  17. OrthogonalLine(E, j) → n
  18. Polygon(B, A, C) → t1, c_1, b, a
  19. Intersect(l, m) → circumcentre
  20. Segment(E, circumcentre) → p
  21. Segment(F, circumcentre) → q
  22. Segment(D, circumcentre) → r
  23. Intersect(l, j) → G
  24. Segment(F, G) → s
  25. Angle(k, s) → α
  26. Intersect(l, i) → H
  27. Segment(F, H) → t
  28. Angle(k, t) → β
  29. Intersect(m, k) → I
  30. Segment(D, I) → d
  31. Angle(d, i) → γ
  32. Intersect(m, j) → J
  33. Segment(J, D) → e
  34. Angle(J, D, A) → δ
  35. Intersect(n, i) → K
  36. Segment(E, K) → f_1
  37. Angle(j, f_1) → ε
  38. Intersect(n, k) → L
  39. Segment(E, L) → g_1
  40. Angle(j, g_1) → ζ
  41. OrthogonalLine(C, i) → h_1
  42. Intersect(f, h_1) → M
  43. Segment(C, M) → i_1
  44. Segment(M, D) → j_1
  45. OrthogonalLine(B, g) → k_1
  46. Intersect(g, k_1) → N
  47. Segment(B, N) → l_1
  48. Segment(N, E) → m_1
  49. OrthogonalLine(A, k) → n_1
  50. Intersect(h, n_1) → O
  51. Segment(O, A) → q_1
  52. Segment(F, O) → p_1
  53. Vector(A, B) → u
  54. Translate(M, u) → M'
  55. Vector(M, M') → v
  56. Angle(B, M, C) → η
  57. Angle(B, N, C) → θ
  58. Angle(C, O, A) → ι
  59. Line(circumcentre, centroid) → r_1
  60. Intersect(n_1, k_1) → P
  61. Segment(O, P) → s_1
  62. Segment(N, P) → t_1
  63. Segment(M, P) → a_1