We start with an acute triangle ABC.
Of the three possible midsegments, we will construct the one parallel to AC.


In steps 1 through 5 which follow, we are constructing the perpendicular bisector of the two sides AB and BC to
get the midpoints of those segments.
This is is the same construction as
Constructing a perpendicular bisector of a segment. 
1. Set the compass width to a little over half the length of AB. 

2. From A, make an arc on each side of AB. 

3. Without changing the compass width, from B, make arcs crossing the first two at E and F.


4. Draw a line from E to F, creating point S where it crosses AB. Point S is the midpoint of AB.


5. Repeat the process with line BC, creating point T on BC.


Now we have the midpoints of AB, BC, we simply link them with a line segment.. 
6. Draw a line from S to T.


Done The segment ST is a midsegment of the triangle ABC.
