**In this assignment we will explore pedal
triangles. Let us first construct a pedal triangle, let triangle
ABC be any triangle and any point p in the plane as shown below.**

**Then we will construct the perpendiculars
from point p to each of the sides of the triangle. It should be
noted that depending on the triangle we may need to extend the
sides so that the perpendiculars will intersect the lines as shown
below.**

**Then finally, construct the points of intersection
of perpendicular lines and the sides of triangle ABC. Use points
SRT as points of intersection as shown above. Then connect this
points (SRT) the triangle obtained, is the pedal triangle which
is colored red blow.**

**If you happen to be interested in more exploration
with working examples in GSP, click here.
For general construction of a pedal triangle RST of triangle ABC
click here for script.**

**What happens when if pedal point p is the
centroid of triangle ABC? If p is in the centroid, then the pedal
triangle becomes orthic triangle. Note that the orthic triangle
is made by connecting the feet of the perpendiculars as shown
below.**

**Try to construct perpendicular lines from
H towards triangle ABC as shown below. It can be noted that the
lines passes through EFG which happen to be the orthic triangle.**

**Now if you consider H as our P, then the
pedal triangle would be like the one seen. Now try to play here with GSP , try to move
P towards H and take note what happens. As P tend toward H It
appear as if the red one will coincide with the blue which is
the orthic triangle. The triangles and perpendiculars begins to
line as illustrated below.**