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A Property of the Equilateral Triangle

A Property of the Equilateral Triangle
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2016-02-14 08:28
TriangleGeometric Construction
This example demonstrates a property of the equilateral triangle, involving concepts such as the properties of an equilateral triangle and distance. By constructing an equilateral triangle ABC and a point D on the ray CB, and the distances from point D to vertices A, B, and C as x, y, and z, the geometric property of the equilateral triangle is illustrated. GeoGebra commands used include Polygon, Ray, Point, Segment, Line, Intersect, and Angle. Suitable for students at the junior high school level and above.

GeoGebra Commands & Parameters

  1. Polygon(B, C, 3) → poly1, a_1, b_1, c_2, A
  2. Ray(C, B) → d
  3. Point(d) → D
  4. Segment(D, A) → a
  5. Segment(D, B) → b
  6. Segment(D, C) → c
  7. Line(D, c_2) → h
  8. Ray(C, A) → i
  9. Intersect(i, h) → E
  10. Polygon(D, E, A) → poly2, c_1, d_1, e_1
  11. Segment(C, E) → e
  12. Angle(poly1) → α, β, γ
  13. Angle(C, D, E) → δ
  14. Angle(D, E, C) → ε
  15. Angle(A, E, D) → ζ