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.


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.