Ruler and Compass Construction 18A
Medians of a Triangle

1. Bisect AB, get midpoint F (construction 1)
2. Median CF
3. Bisect AC, get midpoint I
4. Median BI
5. Medians intersect at J
6. Ray AJ
7. Median AK
Why it works: A median is simply a line from a vertex to the midpoint of the opposite side, so the midpoint construction is applied to two sides. It is theorem that the three medians are concurrent, so the third median can simply be drawn through the intersection of the first two.
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