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Isosceles and Equilateral Triangles - Symmetry Lines

Isosceles and Equilateral Triangles - Symmetry Lines
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2016-07-28 22:51
TriangleGeometric Construction
This example demonstrates the symmetry lines of isosceles and equilateral triangles. It involves core mathematical concepts such as symmetry, isosceles triangles, equilateral triangles, midlines, angle bisectors, intersection, mirroring, and distance. The construction uses GeoGebra commands like Midpoint, Polygon, Line, LineBisector, Intersect, Mirror, and Distance. It is suitable for middle school and above students learning geometric symmetry and transformations, ideal for classroom demonstrations or geometric construction practice.

GeoGebra Commands & Parameters

  1. Midpoint(A, C) → P
  2. Midpoint(C, B) → O
  3. Polygon(C, B, A, D) → poly1, a_1, b_1, d_1, c_1
  4. Line(A, B) → j
  5. Line(D, A) → k
  6. Line(C, B) → l
  7. Line(D, C) → m
  8. LineBisector(M, A) → c
  9. Intersect(c, k) → F_1
  10. Intersect(c, l) → G
  11. Intersect(c, m) → H
  12. Intersect(j, c) → I
  13. Mirror(B, c) → B'
  14. Mirror(D, c) → D'
  15. Mirror(C, c) → A'
  16. Polygon(M, F_1, I) → poly2, i, e, f
  17. Polygon(F_1, D, C, B, I) → poly3, f_1, d, a_2, b_2, i_1
  18. Polygon(F_1, M, B', G) → poly4, f_2, e_1, b', g
  19. Polygon(F_1, D, C, G) → poly5, f_3, d_2, a_3, g_1
  20. Polygon(F_1, M, B', A', H) → poly6, f_4, e_2, b'_1, a', h
  21. Polygon(F_1, D, H) → poly7, h_1, f_5, d_3
  22. Polygon(H, D', M, I) → poly8, h_2, d', e_3, i_2
  23. Polygon(H, C, B, I) → poly9, h_3, a_4, b_3, i_3
  24. Polygon(H, D', M, B', G) → poly10, h_4, d'_1, e_4, b'_2, g_2
  25. Polygon(H, C, G) → poly11, g_3, h_5, a_5
  26. Polygon(G, B, I) → poly13, i_4, g_4, b_4
  27. Polygon(G, A', D', M, I) → poly12, n, p, q, r, s
  28. Midpoint(D, A) → E
  29. Midpoint(C, B) → F
  30. Segment(E, F) → t
  31. If(Distance[M, D] ≤ 0.05, 1, 0) → ok
  32. Midpoint(A, M) → J
  33. Midpoint(b_1) → K
  34. Midpoint(c_1) → L
  35. Line(C, K) → a1
  36. Line(D, B) → c1
  37. Segment(A, C) → e1
  38. Segment(C, B) → f1
  39. Distance(C, B) → cc
  40. Distance(C, A) → bb
  41. Distance(A, B) → aa
  42. Segment(A, B) → a
  43. Segment(C, B) → g1
  44. Midpoint(d_1) → N
  45. Line(A, O) → d1
  46. Line(F_1, B) → b
  47. Line(C, I) → h1
  48. Line(A, O) → i1
  49. Polygon(M, C, O) → poly14, o, m_1, a_6
  50. Line(B, P) → j1
  51. Line(P, B) → b1