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Properties of a Perpendicular Bisector: Dynamic Exploration

Properties of a Perpendicular Bisector: Dynamic Exploration
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2019-03-26 01:31
PolygonCoordinate GeometryTransformationGeometric ConstructionLocus
①This interactive GeoGebra example dynamically demonstrates the key property of a perpendicular bisector: any point on the bisector is equidistant from the endpoints of the segment.②Core mathematical concepts include the definition of a perpendicular bisector, midpoint, distance equality, congruent triangles (used for proof), and symmetry transformations.③Construction highlights: the LineBisector command creates the perpendicular bisector, Midpoint identifies the center, Segment connects points to endpoints, Angle and TableText display measurements, DynamicCoordinates enables dragging point P, and Mirror/Polygon support symmetric constructions. As P moves, lengths AP and BP update in real time, visually confirming equality.④This resource is ideal for middle school geometry lessons on bisector properties and introductory geometric proofs, and also serves as a visual foundation for locus concepts in high school coordinate geometry.

GeoGebra Commands & Parameters

  1. Polygon({(left, bottom), (left, top), (right, top), (right, bottom)}) → viewbox
  2. PointIn(viewbox) → K_P
  3. Mirror(B, yAxis) → A
  4. Segment(A, B) → AB
  5. LineBisector(AB) → perpBisector
  6. LaTeX((((("\text{" * MainInstruc) * "\\") * SpecInstruc) * "}")) → InstrucComplete
  7. DynamicCoordinates(K_P, If[Distance[K_P, perpBisector] < 0.2, 0, x(K_P)], y(K_P)) → P
  8. Segment(B, P) → segAP
  9. Segment(A, P) → segBP
  10. Angle(AB, perpBisector) → α
  11. TableText({{"\text{Segment \(AP\) =}", "\text{Segment \(BP\)=}"}, {("" * segAP), ("" * segBP)}}, "v") → textData
  12. Midpoint(A, B) → center
  13. Segment(A, center) → segAO
  14. Segment((0, 0), B) → segOB