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Pedal Triangle’s

By: Brandie Thrasher

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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

 

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Pedal triangles can be anywhere, inside or outside the original triangle. Let’s 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 BCD’s 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

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Create your own PEDAL TRIANGLE here

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