Assignment #9
Pushing the
Pedal to the Limit!
P is the pedal point of triangle ABC.
RST is the pedal triangle for pedal point P.
When the pedal point is on a side of the triangle ABC, the pedal triangle becomes an obtuse triangle. As the pedal point P approaches any vertex of the triangle, the obtuse angle of the pedal triangle becomes more obtuse. The limit as a pedal point approaches a vertex of the original triangle is a line segment. This limit is called the Simson line.
Another interesting observation regarding the pedal
point is that once the three perpendiculars have passed through any two
vertices of the triangle ABC, the pedal triangle disappears.
PEDAGOGY
Pedal points are not traditionally taught in secondary geometry, even at the honors or gifted level, but some of the properties are very applicable particularly to honors and gifted students because some of these ideas and concepts are good introductions to higher level thinking that will be required in calculus.