by Derelle McFarland
Through the following diagrams I will construct the pedal triangle.
I must begin with the antipedal triangle ABC. By definition the antipedal
triangle A of a given triangle T is the triangle of which T is the pedal
triangle. I'll begin with triangle ABC and pedal point P inside the triangle.
Now, I will construct segments from P perpendicular to sides AB, AC
and BC. Then I will construct a triangle from these points.
This red triangle is the pedal triangle given point P because the vertices
are the feet of the perpendiculars from P to the sides.
I will further investigate the pedal triangle by finding two more pedal
triangles to point P by using the previous steps to find the red pedal triangle.
This is the blue pedal triangle. Now I will construct the third pedal
triangle, a green one.
What do we notice from the first pedal triangle (red) and the second
one (green)? They are similar. This theorem states that the nth pedal n-gon
of any n-gon is similar to the original one.
to Derelle's home page