Department of Mathematics Education
J. Wilson, EMAT 6680


Discovery Within the World of Pedal Triangles Using GSP
by David Wise


For more information on GSP, contact the publisher, Key Curriculum Press. To find instructions on setting up GSP as a helper application click here.

This investigation begins with the construction of a pedal triangle and focuses on the discovery of properties of the pedal triangle when the pedal point is confined to the centroid, incenter, orthocenter, or circumcenter. Centers of triangles are a standard topic in high school geometry courses. Pedal triangle investigations provide interesting extension problems.

I have provided only discoveries. This investigation could easily be adapted for students to follow the same discovery path, or could be altered to investigate one topic with more depth. Students should be able to complete proofs of, or pertaining to relationships discovered within this investigation. In addition, I have only scratch the surface of discoveries based on pedal triangles. For example, when the three vertices of the pedal triangle are collinear (the pedal triangle is degenerate), the line segment is called the Simson Line. The inspiration for this investigation, which suggests many more investigations pertaining to pedal triangles, was developed by Dr. Wilson. Click here to link to his other suggestions for investigations of pedal triangles and the Simson Line.


I. Constructing the Pedal Triangle


II. The pedal point and the centriod of triangle ABC are concurrent.

Findings:

To investigate further, click here for the sketch.


III. The pedal point and the incenter of triangle ABC are concurrent.

Findings:

 

To investigate further, click here for the sketch.


IV. The pedal point and the orthocenter of triangle ABC are concurrent.

Findings:

To investigate further, click here for the sketch.


V. The petal point and circumcenter of triangle ABC are concurrent.

Findings:

 

To investigate further, click here for the sketch.


If you have any comments concerning this investigation that would be useful, especially for use at the high school level, please send e-mail to esiwdivad@yahoo.com.

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