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Equilateral triangles on a triangle

Equilateral triangles on a triangle
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2016-11-25 21:43
TriangleCirclePolygonAngleGeometric Construction
This example demonstrates the process of constructing equilateral triangles inside and outside any given triangle, highlighting geometric properties and constructions. Key math concepts include equilateral triangle construction, angle bisectors, circle-line segment intersections, and polygon drawing. GeoGebra commands used in the construction are Polygon, Circle, Intersect, Segment, Angle, and LineBisector. Suitable for high school geometry instruction, it aids in understanding the symmetry and construction methods of equilateral triangles.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Circle(A, B) → d
  3. Circle(B, A) → e
  4. Circle(C, A) → f
  5. Circle(A, C) → g
  6. Intersect(d, e, 2) → D
  7. Intersect(f, g, 2) → E
  8. Circle(C, B) → h
  9. Circle(B, C) → k
  10. Intersect(h, k, 1) → F
  11. Polygon(A, B, D) → poly2, d_1, a_1, b_1
  12. Polygon(A, E, C) → poly3, c_1, a_2, e_1
  13. Polygon(C, F, B) → poly4, b_2, c_2, f_1
  14. Segment(E, B) → i
  15. Segment(D, C) → j
  16. Segment(F, A) → l
  17. Intersect(b_1, j) → G
  18. Intersect(i, j) → P
  19. Angle(E, P, A) → α
  20. Angle(A, P, D) → β
  21. Angle(D, P, B) → γ
  22. Angle(B, P, F) → δ
  23. Angle(F, P, C) → ε
  24. Angle(C, P, E) → ζ
  25. LineBisector(c) → m
  26. LineBisector(a_1) → n
  27. LineBisector(b_1) → p
  28. LineBisector(c_1) → q
  29. LineBisector(a_2) → r
  30. LineBisector(b) → s
  31. LineBisector(a) → t
  32. LineBisector(c_2) → g_1
  33. LineBisector(b_2) → h_1
  34. Intersect(m, n) → X
  35. Intersect(q, r) → Y
  36. Intersect(t, g_1) → Z
  37. Polygon(X, Y, Z) → poly5, z_1, H, I