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Another Property of Equilateral Triangles

Another Property of Equilateral Triangles
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2017-07-27 01:46
TriangleCircleGeometric Construction
This example demonstrates an additional geometric property of equilateral triangles. It involves core concepts like circles, angle bisectors, polygon construction, and trigonometric relationships. The construction uses commands such as Polygon, Circle, LineBisector, Intersect, Center, CircleArc, Point, Segment, and Distance. Suitable for high school mathematics education, exploring symmetry and relationships between geometric quantities in equilateral triangles.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, f, g, h, C
  2. Circle(A, C, B) → c
  3. LineBisector(A, B) → i
  4. Intersect(c, i, 1) → M
  5. LineBisector(A, C) → j
  6. Intersect(c, j, 2) → N
  7. Center(c) → O
  8. CircleArc(O, B, C) → d
  9. Point(d) → D
  10. Segment(M, D) → k
  11. Segment(N, D) → l
  12. Intersect(h, l) → E
  13. Intersect(f, k) → F
  14. Segment(F, E) → m
  15. Distance(M, F) → MF
  16. Distance(E, N) → EN
  17. Distance(F, E) → FE
  18. Segment(M, O) → n
  19. Segment(O, N) → p
  20. Segment(M, F) → q
  21. Segment(F, O) → r
  22. Segment(O, E) → s
  23. Segment(E, N) → t
  24. Segment(F, D) → b
  25. Segment(D, E) → e
  26. Circle(F, M) → c_1
  27. Circle(E, N) → d_1