Exploring the Simson-Wallace Theorem

Exploring the Simson-Wallace Theorem
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2016-03-04 17:10
This example uses GeoGebra to demonstrate the Simson-Wallace Theorem, which involves the properties of circles and triangles. By constructing the circumcircle of a triangle and the feet of the perpendiculars from a point on the circle to the sides of the triangle, it is shown that these feet are collinear. The example uses commands such as Polygon, Line, OrthogonalLine, Intersect, AreCollinear, Circle, and LocusEquation. Suitable for high school geometry learners and teachers.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  2. Line(B, C) → a
  3. Line(A, C) → b
  4. Line(A, B) → c
  5. OrthogonalLine(D, a) → g
  6. OrthogonalLine(D, b) → h
  7. OrthogonalLine(D, c) → i
  8. Intersect(a, g) → E
  9. Intersect(b, h) → F
  10. Intersect(i, c) → G
  11. AreCollinear(E, F, G) → j
  12. Circle(B, A, C) → k
  13. Line(E, F) → l
  14. Line(F, G) → m
  15. Line(E, G) → n
  16. LocusEquation(AreCollinear[E, F, G], D) → d