Paula Whitmire
Assignment 9
Pedal Triangles
In triangle ABC we will look at any
point P in the plane. Then
the perpendiculars to the sides of
ABC through point P were constructed. These intersections are
R,S,T. The dashed green lines are the perpendicular lines. Triangle
RST is called the Pedal Triangle for the pedal point P.
![](/EMAT6680.2001/Whitmire/lastday/another9/image5.gif)
Next we look at point P outside the
triangle.
Observe what happens when P is on a
vertex. The triangle RST becomes an altitude of triangle ABC.
Move point P outside triangle ABC until
all three vertices of RST are collinear. This is the Simson Line.
Anytime you try to put P on a side
of triangle ABC , P will lie on one of the vertices RST.
The are many more interesting things
to try with the Pedal Point and Pedal Triangle. I enjoyed this
exploration.
RETURN