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Perpendicular Bisector Theorem (Advanced)

Perpendicular Bisector Theorem (Advanced)
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2016-06-20 19:58
TrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the dynamic geometric properties of the perpendicular bisector theorem through interactive operations, visually showing that points on the perpendicular bisector of a segment are equidistant from the segment's endpoints. Core mathematical concepts include perpendicular bisectors, distance formulas, and dynamic geometry. Construction highlights involve GeoGebra commands like Segment, Midpoint, LineBisector, Circle, Intersect, CircleSector, Dilate, Rotate, Point, and Angle. Suitable for high school mathematics instruction to enhance understanding and application of the theorem.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Midpoint(f) → C_1
  3. LineBisector(f) → p
  4. Circle(C_1, (0.1 * f)) → c
  5. Intersect(c, f, 2) → D
  6. Intersect(c, p, 2) → E
  7. CircleSector(C_1, D, E) → d
  8. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], C_1) → A'
  9. Segment(A, A') → h
  10. Dilate(C_1, If[1 < a ≤ 2, 2 - a, 0], B) → C'
  11. Segment(C_1, C') → i
  12. Rotate(A, If[2 < a ≤ 3, ((-(a - 2)) * π), (-π)], C_1) → A'_1
  13. Rotate(A', If[2 < a ≤ 3, ((a - 2) * π), π], C_1) → A''
  14. Segment(A'_1, A'') → h'
  15. Rotate(d, If[3 < a ≤ 4, ((a - 3) * π / 2), π / 2], C_1) → d'
  16. Point(p) → C
  17. Dilate(A, If[4 < a ≤ 5, 5 - a, 0], C) → A'_2
  18. Segment(A, A'_2) → g
  19. Dilate(B, If[5 < a ≤ 6, 6 - a, 0], C) → B'
  20. Segment(B, B') → j
  21. Angle(A, C, B) → α
  22. Rotate(A, If[6 < a ≤ 7, ((a - 6) * α), α], C) → A'_3
  23. Rotate(A'_2, If[6 < a ≤ 7, ((a - 6) * α), α], C) → G
  24. Segment(A'_3, G) → g'