In this exercise we will be using pedal triangles to do different explorations.
First, I will explain how to construct a pedal triangle. I started with a triangle (ABC) and an arbitrary point outside the triangle which I called the pedal point. Then I constructed perpendicular lines to each of the sides of ABC which passed through the pedal point. The intersection of the extended lines of ABC and the perpendicular lines gave me my pedal triangle DEF.
To use this script tool click here.
Now lets see what happens when the pedal point is the centroid of the triangle ABC. First I will construct the centroid then overlap the two points.
The new triangle formed looks like it might be an isoceles triangle. Lets measure the length of the sides to find out!
Even though it looks like an isoceles triangle it is not because two of the sides of the triangle do not have equal length.