In parallelogram $ABCD$,$AB = 12.5 \, cm$ and $BC = 7 \, cm$,then find the perimeter of $ABCD$ in $cm$.

$E$ is the mid-point of the side $AD$ of the trapezium $ABCD$ with $AB \parallel DC$. $A$ line through $E$ drawn parallel to $AB$ intersects $BC$ at $F$. Show that $F$ is the mid-point of $BC$.

In trapezium $ABCD$,$AB \parallel CD$. If $\angle A = 70^{\circ}$ and $\angle B = 85^{\circ}$,then $\angle D = \ldots$ (in $^{\circ}$)

In parallelogram $PQRS$,the bisector of $\angle P$ intersects $RS$ at $M$ and the bisector of $\angle R$ intersects $PQ$ at $N$. Prove that $PNRM$ is a parallelogram.

$A$ square is inscribed in an isosceles right triangle so that the square and the triangle have one angle common. Show that the vertex of the square opposite the vertex of the common angle bisects the hypotenuse.

Which of the following is not true for a parallelogram?