$ABCD$ is a quadrilateral in which $P$, $Q$, $R$ and $S$ are the mid-points of sides $AB$, $BC$, $CD$ and $DA$ respectively. Then $PQRS$ is a:

According to Varignon's Theorem, the quadrilateral formed by joining the mid-points of the consecutive sides of any arbitrary quadrilateral is always a parallelogram.
By drawing diagonal $AC$, in $△ABC$, $P$ and $Q$ are midpoints, so $PQ\parallel AC$ and $PQ=\frac{1}{2}AC$ (by Midpoint Theorem). Similarly, in $△ADC$, $S$ and $R$ are midpoints, so $SR\parallel AC$ and $SR=\frac{1}{2}AC$. Thus, $PQ\parallel SR$ and $PQ=SR$, making $PQRS$ a parallelogram.