Pedal
Triangles

(Assignment 9)

**by**

Robin Kirkham, J. Matt Tumlin, and Cara Haskins

A ** Pedal Triangle** is formed
from the following construction.

Let
triangle **ABC,** be any triangle. If **P** is any point in the plane, then
the triangle formed by constructing perpendiculars to the sides of **ABC **locate** **three points **R**, **S**, and **T** that are the
intersections. Triangle **RST** is the ** Pedal Triangle **for

First we will
examine triangle **ABC**** **with point **P** in the plane, and its perpendiculars
to the sides of **ABC**** **that creates the *Pedal Triangle***RST****. **

** **

Now we will
examine what happens to triangle **RST**, if **P** is on the
side of triangle **ABC**:

Regardless of where it is placed on the
side, you will notice that **P** becomes one of the vertices of
triangle **RST****. **

Now let us
examine what happens with triangle **RST****,** if **P** is placed at
one of the vertices of triangle **ABC**:

Regardless of
which vertex is used, you will notice that triangle **RST** collapses to
one of the perpendicular bisectors of triangle **ABC**.