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Converse of the Perpendicular Bisector Theorem Illustrated

Converse of the Perpendicular Bisector Theorem Illustrated
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2015-11-26 06:58
TriangleCoordinate GeometryGeometric Construction
This example illustrates the Converse of the Perpendicular Bisector Theorem: if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Key math concepts include segments, midpoints, perpendicular bisectors, distances, and angles. Construction highlights the use of GeoGebra commands like Segment, Midpoint, LineBisector, Point, Angle, OrthogonalLine, and Distance. Suitable for high school mathematics instruction and geometric construction practice.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Midpoint(a) → M
  3. LineBisector(A, B) → b
  4. Point(b) → D
  5. Segment(A, D) → c
  6. Segment(D, B) → d
  7. Angle(D, M, B) → α
  8. Segment(A, M) → e
  9. Segment(M, B) → f
  10. Point(b) → E
  11. Point(b) → F
  12. Segment(E, F) → g
  13. Point(g) → C
  14. Segment(A, P) → h
  15. Segment(P, B) → i
  16. Segment(A, P) → j
  17. Segment(P, B) → k
  18. Segment(A', B') → l
  19. Midpoint(l) → M'
  20. OrthogonalLine(M', l) → m
  21. Point(m) → J
  22. Point(m) → K
  23. Segment(J, K) → n
  24. Segment(A', M') → p
  25. Segment(M', B') → q
  26. Distance(p, q) → o
  27. Point(n) → P'
  28. Segment(A', P') → r
  29. Segment(P', B') → s
  30. Distance(r, s) → t
  31. Angle(P', M', B') → β
  32. Point(n) → C'