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Construction of Angle Bisector Using Compasses

Construction of Angle Bisector Using Compasses
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2017-11-28 21:00
CircleAngleGeometric Construction
In collections Mathematics Form 1
This example demonstrates how to construct an angle bisector of any angle using compasses and straightedge. The core mathematical concepts involved include angles, geometric construction, midpoint, and circles. Key construction steps involve using commands like Circle, Rotate, Midpoint, AngularBisector, and Intersect. It is suitable for middle school students and above to learn geometric construction techniques and deepen their understanding of the properties of angle bisectors.

GeoGebra Commands & Parameters

  1. Circle(O, Distance[O, B]) → s
  2. Rotate(B, 170°, O) → B'
  3. Circle(O, B) → c
  4. Arc(c, B, B') → d
  5. Point(d) → A
  6. Midpoint(O, A) → G
  7. AngularBisector(B, O, A) → j
  8. Intersect(s, j, 2) → F
  9. Segment(O, B) → f
  10. Segment(O, A) → g
  11. Circle(O, R_1) → e
  12. If(0 ≤ a < 1, a, 1) → m_1
  13. Angle(B, O, A) → α
  14. Intersect(e, g, 1) → C
  15. Intersect(e, f, 1) → D
  16. Rotate(C, 15°, O) → C'
  17. If(1 ≤ a < 2, a - 1, If[a < 1, 0, 1]) → m_2
  18. If(2 ≤ a < 3, a - 2, If[a < 2, 0, 1]) → m_3
  19. Rotate(C', (((-m_1) * (α / ° + 30)))°, O) → D'
  20. Arc(e, D', C') → h
  21. Distance(G, F) → R_2
  22. Circle(C, R_2) → k
  23. Circle(D, R_2) → p
  24. Intersect(k, p, 1) → E
  25. Rotate(E, 15°, C) → E'
  26. Rotate(E', (((-m_2) * 30))°, C) → E_1
  27. Arc(k, E_1, E') → q
  28. Rotate(E, 15°, D) → E''
  29. Rotate(E'', (((-m_3) * 30))°, D) → E_2
  30. Arc(p, E_2, E'') → r
  31. Vector(O, E) → u
  32. If(3 ≤ a ≤ 4, a - 3, 0) → m_4
  33. Translate(O, Vector[(m_4 * u)]) → O'
  34. Segment(O, O') → i
  35. Angle(D', O, C') → β
  36. SelectedIndex(Bahasa) → n
  37. If(n ≟ 1, "Animate", "Animasi") → Tex1
  38. If(n ≟ 1, "Resume", "Teruskan") → Tex3
  39. If(n ≟ 1, "Reset", "Semula") → Tex8
  40. If(n ≟ 1, "Stop", "Berhenti") → Tex2
  41. If(n ≟ 1, "To construct the angle bisector of ∠AOB using a pair of compasses", "Membina pembahagi dua sama ∠AOB dengan menggunakan jangka lukis") → Tex4
  42. If(n ≟ 1, "Center O radius less than OA", "Pusat O jejari kurang daripada OA") → Tex5
  43. If(n ≟ 1, "Center C suitable radius R", "Pusat C jejari yang sesuai R") → Tex6
  44. If(n ≟ 1, "Center D radius R", "Pusat D jejari R") → Tex7

AI Drawing Prompt Reference

Construct the angle bisector of ∠AOB using a pair of compasses. First, draw a circle with center O and radius less than OA, intersecting the sides of ∠AOB at points C and D. Then, draw circles with centers C and D and appropriate radii, intersecting at point E. Next, draw a circle with center E and radius OE, intersecting the previous circle at point F. Finally, draw a circle with center O and radius OF, intersecting the sides of ∠AOB at points G and H, and connect OG and OH to form the angle bisector.
The prompt above was compiled from the original drawing commands and is for reference only.