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Perpendicular Bisector Construction by Julian Smith

Perpendicular Bisector Construction by Julian Smith
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2015-04-14 11:02
CircleAngleGeometric Construction
This example demonstrates how to construct a perpendicular bisector using geometric methods. Key mathematical concepts include the perpendicular bisector of a line segment, properties of circles, and distance calculations. Construction involves GeoGebra commands such as Segment, Circle, Intersect, Line, Distance, and Angle, along with objects like A, B, a, c, d, E, F, G. Suitable for middle school students learning geometry fundamentals or for educational demonstrations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Circle(A, 8) → c
  3. Circle(B, 8) → d
  4. Intersect(c, d, 1) → C
  5. Intersect(c, d, 2) → D
  6. Line(C, D) → b
  7. Distance(A, B) → distanceAB
  8. Intersect(b, a) → E
  9. Angle(C, E, A) → α
  10. Circle(F, G) → e
  11. Circle(G, F) → f
  12. Intersect(e, f, 1) → H
  13. Segment(H, F) → g
  14. Segment(F, G) → h
  15. Segment(G, H) → i
  16. Distance(F, G) → distanceFG
  17. Distance(G, H) → distanceGH
  18. Distance(H, F) → distanceHF
  19. Segment(I, J) → j
  20. Segment(K, J) → k
  21. Circle(J, L) → p
  22. Intersect(p, j, 1) → M
  23. Intersect(p, k, 1) → N
  24. Circle(M, 6) → q
  25. Circle(N, 6) → r
  26. Intersect(q, r, 1) → O
  27. Angle(N, J, O) → β
  28. Angle(O, J, M) → γ
  29. Segment(J, O) → l

AI Drawing Prompt Reference

Construct the perpendicular bisector of line segment AB. First, draw two circles with centers A and B and the same radius, find their intersection points C and D, then connect C and D to get the perpendicular bisector b. Measure the length of line segment AB, find the intersection point E of the perpendicular bisector b and line segment AB. Further construct angle α, and draw circles e and f with centers E, find their intersection point H, then connect H and E to get line segment g. Measure the length of line segment EF, construct circles p with centers F and G, find their intersection points M and N, then construct circles q and r with centers M and N, find their intersection point O, finally construct angles β and γ.
The prompt above was compiled from the original drawing commands and is for reference only.