7. Construct a Triangle Given the Lengths of Two Sides and a Median of the Third Side

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This Demonstration shows a construction of a triangle given the lengths of two sides and and the length of the median from to .



Let be a line segment of length and midpoint .

Step 2: Extend past to such that . The triangle has side of length , since is a parallelogram with sides and . Similarly, . Finally, is a median of length .


Contributed by: Izidor Hafner (August 2017)
Open content licensed under CC BY-NC-SA



With the condition , the problem has a solution iff [1, pp. 287–288].


[1] A. McFarland, J. McFarland and J. T. Smith, eds., Alfred Tarski, Early Work in Poland—Geometry and Teaching, New York: Birkhäuser, 2014.

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