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Rotation and Intersection of Equilateral Triangles

Rotation and Intersection of Equilateral Triangles
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2015-06-23 08:40
TriangleCoordinate Geometry
In collections Constructions for Problem Set 2
This example demonstrates the rotation of equilateral triangles and the construction of their intersection points. Key mathematical concepts include the properties of equilateral triangles, rotation transformations, and intersection. GeoGebra commands used include Intersect, Point, Segment, Rotate, and Angle. Suitable for high school mathematics education, particularly in coordinate geometry and geometric construction.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(Circle[A, 1]) → B
  3. Segment(A, B) → c
  4. Point(Circle[B, 1.7320508075688772]) → C
  5. Segment(B, C) → d
  6. Rotate(B, 90*°, B) → B'
  7. Rotate(C, 90*°, B) → C'
  8. Segment(B', C') → d'
  9. Angle(C, B, a) → α
  10. Point(Circle[a, -3.4641016151377544]) → D
  11. Segment(a, D) → e
  12. Point(Circle[D, -2]) → E
  13. Segment(D, E) → f
  14. Rotate(D, 90*°, D) → D'
  15. Rotate(E, 90*°, D) → E'
  16. Segment(D', E') → f'
  17. Angle(E', D, a) → β