Pedal Triangles


Kimberly N. Bennekin

Let triangle ABC be any triangle. Then if P is any point in the plane, then the triangle formed by constructing perpendiculars to the sides of ABC (extended if neccessary) locate three points R, S, and T that are the intersections. Triangle RST is the Pedal Triangle for the Pedal Point P.

Use GSP to create a script for the general construction of a pedal triangle RST where P is any point in the plane of ABC.

Pedal Triangle

What if the Pedal point is chosen to be one of the sides of the triangle? Consider the following:

A vertex of the Pedal triangle occurs at the Pedal point.

What if the Pedal point is chosen as one of the verticies of the triangle ABC? Consider the following:

If the Pedal point is a vertex of the triangle ABC, then a pedal triangle does not exist. It is just a line segment.

Many explorations can be made with Pedal triangles using the script shown above and GSP.

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