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Perpendicular Bisector Construction by Alexander Lau

Perpendicular Bisector Construction by Alexander Lau
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2014-03-23 16:38
AngleCoordinate GeometryGeometric Construction
In collections Special Lines and Centres of Triangle
This example demonstrates the construction of a perpendicular bisector. Key mathematical concepts include the perpendicular bisector of a line segment and the property that points on the bisector are equidistant from the endpoints of the segment. The construction uses commands such as Polygon, LineBisector, Point, Intersect, Segment, Angle, Circle, and Midpoint. Suitable for students in middle school and above learning geometric construction.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. LineBisector(a) → d
  3. LineBisector(c) → e
  4. LineBisector(b) → f
  5. Point(f) → D
  6. Intersect(f, b) → E
  7. Point(e) → F
  8. Intersect(e, c) → G
  9. Point(d) → H
  10. Intersect(d, a) → I
  11. Segment(H, I) → g
  12. Segment(D, E) → h
  13. Segment(F, G) → i
  14. Angle(D, E, C) → α
  15. Angle(B, G, F) → β
  16. Angle(C, I, H) → γ
  17. Intersect(d, h) → O
  18. Segment(H, I) → j
  19. Point(d) → J
  20. Segment(I, J) → k
  21. Circle(O, A) → p
  22. Midpoint(A, B) → K
  23. Midpoint(B, C) → L
  24. Midpoint(A, C) → M

AI Drawing Prompt Reference

Draw a triangle ABC, find the midpoints K, L, M of sides AB, BC, AC respectively, then draw the perpendicular bisectors of these sides, mark the intersection points of the bisectors as D, E, F, connect DE, EF, FD to form triangle DEF, measure the angles DEF, EFD, FDE, then draw the perpendicular bisectors of line segments DE and DF and mark their intersection point as O, finally draw a circle with O as the center and A as the radius.
The prompt above was compiled from the original drawing commands and is for reference only.