37. Given a segment and a line parallel to it. Using only a ruler, divide the segment in half.
37. Let a segment $A B$ and a line $l$ parallel to it be given. Take an arbitrary point $P$ outside the strip bounded by the lines $A B$ and $l$, and draw the lines $P A$ and $P B$, and denote by $D$ and $C$ the points of intersection of these lines with the line $l$. In the resulting trapezoid $A B C D$, draw the diagonals $A C$ and $B D$, and denote their intersection point by $O$. The line $P O$ will intersect the segment $A B$ (the base of the trapezoid) at its midpoint $M$. The entire construction is done with a single ruler.