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Proof Prompt: Perpendicular Lines

Proof Prompt: Perpendicular Lines
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2016-10-19 07:45
AngleCoordinate GeometryGeometric Construction
This example demonstrates that when two lines intersect to form congruent adjacent angles, the lines are perpendicular. Key mathematical concepts include angles, intersection, and straight lines. GeoGebra commands used include Line, Intersect, OrthogonalLine, etc. Suitable for middle school and above students to learn geometric proofs.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Circle(A, 1) → c
  3. Circle(B, 1) → d
  4. Intersect(d, f, 2) → C
  5. Intersect(c, f, 1) → D
  6. Ray(B, C) → g
  7. Ray(A, D) → h
  8. Segment(A, B) → i
  9. Point(i) → E
  10. Segment(E, B) → j
  11. Segment(E, A) → k
  12. OrthogonalLine(E, j) → l
  13. Min(k, j) → a
  14. Circle(E, (0.3 * a)) → e
  15. Intersect(e, j, 1) → F
  16. Intersect(e, l, 2) → G
  17. CircleSector(E, F, G) → p
  18. Intersect(e, k, 1) → H
  19. Intersect(e, l, 1) → I
  20. Point(l) → J
  21. Rotate(p, If[0 < b ≤ 1, (b * π / 2), π / 2], E) → p'
  22. Angle(J, E, B) → α