Making a Unique Triangle


By: Carly Cantrell


Given three line segments AB, BC, and CA. These are the medians of a triangle, how can you construct the triangle?


To construct the unique triangle with the given medians:


Given medians AB, BC, and AC:


1.  Create a triangle using the medians.


2.  Construct two medians in your created triangle. Construct AD and BE.


3.  Make a point O where these two medians intersect.



4.  Using a compass, or GSP, extend AD to a new point, F. Such that, OD = DF



5.  Make a segment from F to C, FC.


6.  Using a compass, or GSP, extend FC to a new point, G. Such that, FC = CG



7.  Thus, triangle AFG is constructed.



Following this method, if you were given any three medians then you could always create the parent triangle!


You can use the color-coded segments to visually see the representation:


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