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: