Pedal Triangles

by Zack Kroll

Pedal triangles sound like they should be related to flowers or at least resemble parts of a flower. In fact pedal triangles are triangles that can be constructed using a triangles and series of perpendicular lines.

This link contains a script for how to construct a pedal triangle.

The fascinating part about a pedal triangle is what occurs when we manipulate point P. First, let's observe what happens when the pedal point P is located outside of the triangle. The pedal triangle allows flips outside the triangle. The example on the right; however, is different than the first one. When the pedal point is located to left of the triangle, part of the pedal triangle is located inside while the rest is outside of the original triangle.

What happens when P is on the side of the triangle? Does it change depending upon what side it is?

As we can see when we place the pedal point on any of the three side of the triangle, the pedal triangle is located inside that triangle. Furthermore, one of the vertices and the pedal point merge together on that side.

What happens now when the pedal point is on one of the vertices?

When the pedal point is located at any one of the three vertices of the triangle All three vertices of the pedal triangle as well as the pedal point converge at the vertex of the original triangle. In addition, perpendicular lines are formed and intersect at this point.