Investigation Nine
Pedal Triangles
Charles Meyer
In this investigation I will look at the pedal triangle. Along
the way I hope to educate the reader on its orgins as well as
its different properties.
A pedal triangle is formed from the perpendiculars of a given
triangle to a point P in the plane, then the intersection of triangle
ABC to the perpendiculars will form a triangle.
Let's begin with the triangle ABC and Point B.
![](image16.gif)
Now we must create the perpendiculars from each segment of
ABC to point P.
![](image17.gif)
The intersections of the segments and the perpendiculars are
now found and labeled TSR so that the triangle TSR is the pedal
triangle of point P.
![](image18.gif)
![](image19.gif)
Below are example of the the point P being within different
parts of the triangle. There is not much overall difference to
the triangle at the different points other than size of interior
angles.
![](image20.gif)
![](image21.gif)
What is really fascinating is the fact that the point P can
also lie outside the triangle as shown below and still a triangle
can be found.
![](image22.gif)
However at some point the triangle is lost as the perpendicular
intersections are unable to form a triangle.
![](image23.gif)
The study of pedal triangles may be helpful to high school
geometry students who are trying to find interesting parts of
triangle construction.