We start with the triangle PQR.
The median of a triangle
is a line segment
linking the midpoint of a side to the opposite
vertex.
There are therefore three possible medians, and this shows one of them. The other two can be drawn in a similar fashion.


In the first four steps we create the
perpendicular bisector of PQ.
See Constructing a perpendicular bisector of a line segment.
This establishes the midpoint of a side. 
1. With the compasses' point on any vertex, set the compasses' width to any medium setting.
In this example, we pick point P and the side PQ. 

2. Draw an arc on each side of the line. 

3. Without changing the compasses' width, place the compasses' point on the other end of the selected side,
and make two more arcs so they intersect with the first two. 

4. Draw a line between the points where the arcs cross.
This will bisect the triangle side, dividing it into two equal parts.
Label this point S. 

We then simply draw a line from this midpoint to the opposite vertex. 
5. Draw a line between S and the vertex opposite  in this case the point R. 

6. Done. The blue line SR is one of the three possible medians of the triangle PQR.
The other two can be constructed in a similar way 
