Pedal TriangleÕs

By: Brandie Thrasher

A pedal triangle is formed from
taking a triangle, lets say ABC

Find any point in the plane; we
will call our point p

Now, we construct a triangle from the
sides of ABC

With all points present, we can now
construct our triangle RST, the pedal triangle

Pedal triangles can be anywhere,
inside or outside the original triangle. LetÕs investigate some other
properties of pedal triangles by using the centroid of triangle ABC, and seeing
if the point (labeled P) will be the point that yields a pedal triangle. We
will construct our triangle using the script tool btcentroid.

Here, I have also labeled the
midpoints of the line segments, as E, F, and G and point P is where the median
lines of the midpoints intersect. To from the pedal triangle we will construct
just as earlier, based on point P.

And our final inscribed pedal
triangle looks like this.

Triangle RST appears to be just shy
of involving three of triangle BCDÕs midpoints. We can make some conjectures
about our pedal triangle that could be later investigated, using proof.

1. Triangle RST is similar to triangle
BCD

2. Triangle
RST is comprised of three triangles, PRS, PST, and PTR

3. Triangle
PRS is similar to triangle PTR

Create your own PEDAL TRIANGLE here