The perimeter of rectangle $ABCD$ is $112 \, cm$ and $AB : BC = 5 : 3$. Find the length of $AB$ in $cm$.

Show that the quadrilateral formed by joining the mid-points of the sides of a rhombus,taken in order,is a rectangle.

$A$ diagonal of a rectangle is inclined to one side of the rectangle at $25^{\circ}$. The acute angle between the diagonals is (in $^{\circ}$)

$PQ$ and $RS$ are two equal and parallel line segments. Any point $M$ not lying on $PQ$ or $RS$ is joined to $Q$ and $S$. Lines are drawn through $P$ parallel to $QM$ and through $R$ parallel to $SM$,meeting at $N$. Prove that line segments $MN$ and $PQ$ are equal and parallel to each other.

In quadrilateral $PQRS$,the bisectors of $\angle P$ and $\angle Q$ intersect at $M$. Prove that $\angle S + \angle R = 2 \angle PMQ$.

Three angles of a quadrilateral $ABCD$ are equal. Is it a parallelogram? Why or why not?