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

The angle between two altitudes of a parallelogram drawn from the vertex of an obtuse angle is $60^{\circ}$. Find the angles of the parallelogram.

$(1)$ $A$ quadrilateral has ......... pairs of consecutive angles.
$(2)$ The sum of measures of all the four angles of a quadrilateral is ...........

Show that the quadrilateral formed by joining the mid-points of the consecutive sides of a square is also a square.

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

$E$ and $F$ are points on diagonal $AC$ of a parallelogram $ABCD$ such that $AE = CF$. Show that $BFDE$ is a parallelogram.