Pedal Triangles

By: Kimberly Young and Mindy Swain

Investigating Pedal Triangles.

First construct a pedal triangle: 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 locate three points R, S, and T that are intersections. Triangle RST is the Pedal triangle for Pedal Point P. This is an example of a Pedal Triangle.

Click Here

What happens to P if P is on the side of triangle ABC?

When P is on the side of the triangle, an image as below is constructed. Click Here and drag the labeled point to see how the shape of the petal triangle changes as the point changes.

As you drag the point, you will notice that as it approaches either vertex, the pedal triangle's area gets smaller. It looks like the triangle will become a line when the point is on the vertex. Change the size of the original triangle and see if this is still true. Click Here.

Lets take a look closer to see what happens at the vertices.

What happens to P it P is on the vertex of triangle ABC?

When the pedal triangle is constructed using the vertex as the point P, a line segment is form.