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.

Now we must create the perpendiculars from each segment of ABC to point P.

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.

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.

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.

However at some point the triangle is lost as the perpendicular intersections are unable to form a triangle.

The study of pedal triangles may be helpful to high school geometry students who are trying to find interesting parts of triangle construction.


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