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Constructing an Equilateral Triangle with Compass and Straightedge

Constructing an Equilateral Triangle with Compass and Straightedge
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2017-02-18 03:18
TriangleCircleGeometric Construction
This example demonstrates how to construct an equilateral triangle using a compass and straightedge. Key mathematical concepts include geometric construction and transformation. Using GeoGebra commands such as Dilate, Segment, Circle, and Rotate, the triangle can be dynamically modified. Suitable for middle school and above students learning geometric construction and transformation.

GeoGebra Commands & Parameters

  1. Dilate(A, If[0 < b ≤ 1, 1 - b, 0], B) → A'
  2. Segment(A, A') → f
  3. Circle(A, B) → c
  4. Circle(B, A) → d
  5. Rotate(B, If[1 < b ≤ 2, (((b - 1) * 2) * π), (2 * π)], A) → B'
  6. CircleArc(A, B, B') → e
  7. Intersect(c, d, 1) → C
  8. Intersect(c, d, 2) → D
  9. Rotate(A, If[1 < b ≤ 2, (((b - 1) * 2) * π), (2 * π)], A) → A'_1
  10. Rotate(A', If[1 < b ≤ 2, (((b - 1) * 2) * π), (2 * π)], A) → A''
  11. Segment(A'_1, A'') → f'
  12. Rotate(A, If[2.5 < b ≤ 3.5, (((b - 2.5) * 2) * π), (2 * π)], B) → A'_2
  13. CircleArc(B, A, A'_2) → g
  14. Rotate(B, If[3.5 < b ≤ 4.5, ((b - 3.5) * π / 3), π / 3], A) → B'_1
  15. Rotate(A, If[3.5 < b ≤ 4.5, ((b - 3.5) * π / 3), π / 3], A) → A'_3
  16. Rotate(A', If[3.5 < b ≤ 4.5, ((b - 3.5) * π / 3), π / 3], A) → A''_1
  17. Segment(A'_3, A''_1) → f'_1
  18. Rotate(A, If[4.5 < b ≤ 5.5, ((-(b - 4.5)) * π / 3), ((-π)) / 3], B) → A'_4
  19. Rotate(A', If[4.5 < b ≤ 5.5, ((-(b - 4.5)) * π / 3), ((-π)) / 3], B) → A''_2
  20. Segment(A'_4, A''_2) → f'_2
  21. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  22. Rotate(A, If[2.5 < b ≤ 3.5, (((b - 2.5) * 2) * π), (2 * π)], B) → A'_5
  23. Rotate(A', If[2.5 < b ≤ 3.5, (((b - 2.5) * 2) * π), (2 * π)], B) → A''_3
  24. Segment(A'_5, A''_3) → f'_3