ASSIGNMENT NINE
Problem #1a,b & #4



 

The purpose of this investigation is to explore the Pedal Triangle that is constructed by point P outside a given triangle and the perpediculars from P to the sides of the given triangle.

 

Suppose point P is in the exterior of the given triangle (in black). Then the Pedal Triangle to the Pedal Point P is as follows (in yellow):

 


 

Note that at least one of the vertices of the Pedal Triangle is on a side of the given triangle.

Now, suppose that the Pedal Point P is in the interior of the given triangle. Then the Pedal Triangle to Pedal Point P is in yellow as follows:


 

Note that all three vertices of the Pedal Triangle are part of the three sides of the given triangle.

 

Suppose that pedal point P is the Orthocenter of the given triangle. Then the Pedal Triangle to Pedal Point P is the given triangle. (To further investigate the implications of the Pedal Triangle to Pedal Point P as the Orthocenter to the given triangle, click here.

 
 

 

To explore further the implications of Pedal Point P to the Pedal Triangle, click here.

 

At this point of this investigation, I would require my students to examine different locations of the pedal point to the pedal triangle and the given triangle. I would ask them to discuss such cases as P as incenter, centroid, circumcenter, etc.


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