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Construction of 60° Using Compasses

Construction of 60° Using Compasses
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2017-11-28 20:56
TriangleCircleAngleTransformationGeometric Construction
In collections Mathematics Form 1
①This example demonstrates how to construct a 60° angle using only compasses (no marked ruler), with interactive buttons and dynamic text explanations. ②The core mathematical concept is the property of an equilateral triangle: since all three sides are equal, each interior angle is 60°, so constructing an equilateral triangle yields the desired angle. ③Construction details: from the summary, commands such as Segment, Point, and Circle are used; a circle is drawn with center O and radius OA, then another circle with center A and the same radius; their intersection P with O and A forms an equilateral triangle, giving the 60° angle. Additional commands like If, Vector, Translate, and SelectedIndex enable dynamic step-by-step demonstration and button controls, with multiple text objects (Tex1~Tex6) labeling angles and steps. ④This is suitable for middle school geometry lessons on compass-and-straightedge constructions, and serves as a reference for designing interactive GeoGebra worksheets.

GeoGebra Commands & Parameters

  1. Segment(O, A) → f
  2. Point(f) → P
  3. Circle(O, P) → e
  4. If(a ≟ true, Rotate[P, 100°, O], Rotate[P, -100°, O]) → P'
  5. If(a ≟ true, Rotate[A, 60°, O], Rotate[A, -60°, O]) → B'
  6. Circle(P, O) → h
  7. If(a ≟ true, Rotate[O, -40°, P], Rotate[O, 40°, P]) → C
  8. If(a ≟ true, Rotate[O, (-β), P], Rotate[O, β, P]) → E
  9. If(a ≟ true, Arc[h, E, C], Arc[h, C, E]) → k
  10. If(a ≟ true, Rotate[P, α, O], Rotate[P, (-α), O]) → D
  11. If(a ≟ true, Arc[e, P, D], Arc[e, D, P]) → c
  12. Vector(O, B') → u
  13. Translate(O, Vector[(b * u)]) → O'
  14. Segment(O, O') → g
  15. If(a ≟ true, Angle[A, O, B'], Angle[B', O, A]) → γ
  16. SelectedIndex(Bahasa) → nn
  17. If(nn ≟ 1, "Animate", "Animasi") → Tex1
  18. If(nn ≟ 1, "Stop", "Berhenti") → Tex2
  19. If(nn ≟ 1, "Resume", "Teruskan") → Tex3
  20. If(nn ≟ 1, "Center O Radius OP", "Pusat O Jejari OP") → Tex4
  21. If(nn ≟ 1, "Center P Radius OP", "Pusat P Jejari OP") → Tex5
  22. If(nn ≟ 1, "To construct an angle of 60° at O using a pair of compasses", "Membina sudut 60° pada O dengan menggunakan jangka lukis") → Tex6

AI Drawing Prompt Reference

Construct a 60-degree angle using only a compass. Draw a horizontal segment with left endpoint O and right endpoint A. Draw a circle centered at O with radius OA, then another circle centered at A with the same radius. The two circles intersect at a point above the segment. Connect O, A, and the intersection to form an equilateral triangle, so the angle at O is 60 degrees. Include interactive controls for step-by-step animation and text labels explaining each step.
The prompt above was compiled from the original drawing commands and is for reference only.