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Construct a Perpendicular Line with Compass and Straightedge

Construct a Perpendicular Line with Compass and Straightedge
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2015-02-18 02:20
Coordinate GeometryTransformationGeometric Construction
In collections PARCC Math III Unit 5 Lesson 1
This example demonstrates how to construct a perpendicular line through a point B not on a given line m using a compass and straightedge. Key mathematical concepts include geometric construction. The example uses commands such as Polygon, Line, Point, Circle, Intersect, Mirror, OrthogonalLine, and CircumcircleArc in GeoGebra. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon((22, y(Corner[1])), Corner[2], Corner[3], (22, y(Corner[4]))) → mask, a, b, c, d
  2. Line(Point_1, Point_2) → BaseLine
  3. Point(BaseLine) → D
  4. Circle(B, D) → CircB
  5. Intersect(CircB, BaseLine) → G, F
  6. Mirror(B, BaseLine) → H
  7. Circle(G, B) → CircG
  8. Circle(F, B) → CircF
  9. OrthogonalLine(G, BaseLine) → PerpLineG
  10. OrthogonalLine(F, BaseLine) → PerpLineF
  11. Intersect(CircF, PerpLineF) → ArcFa, ArcFb
  12. Intersect(CircG, PerpLineG) → ArcGb, ArcGa
  13. CircumcircleArc(ArcGa, B, ArcGb) → ArcG
  14. CircumcircleArc(ArcFb, B, ArcFa) → ArcF
  15. Line(B, H) → PerpLine
  16. OrthogonalLine(B, PerpLine) → ParLineB
  17. Intersect(CircB, ParLineB) → ArcBb, ArcBa
  18. CircumcircleArc(ArcBb, F, ArcBa) → ArcB