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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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