The quadrilateral formed by joining the mid-points of the sides of a quadrilateral $PQRS$, taken in order, is a rhombus, if

If bisectors of $\angle A$ and $\angle B$ of a quadrilateral $ABCD$ intersect each other at $P\mathit{,}$ bisectors of $\angle B$ and $\angle C$ at $Q,$ bisectors of $\angle C$ and $\angle D$ meet at $R$ and bisectors of $\angle D$ and $\angle A$ meet at $S$, then $PQRS$ is a