In quadrilateral $ABCD$,$\angle A + \angle D = 180^{\circ}$. What special name can be given to this quadrilateral?

In $\Delta ABC$,$AD$ is a median and $E$ is the midpoint of $AD$. $BE$ is extended to intersect $AC$ at $F$. Prove that $AF = \frac{1}{3} AC$.

Through $A, B$ and $C$,lines $RQ, PR$ and $QP$ have been drawn,respectively parallel to sides $BC, CA$ and $AB$ of a $\triangle ABC$ as shown in the figure. Show that $BC = \frac{1}{2} QR$.

The figure formed by joining the mid-points of the sides of a quadrilateral $ABCD,$ taken in order,is a square only if,

In $\Delta PQR$,$A$,$B$,and $C$ are the mid-points of $PQ$,$QR$,and $RP$ respectively. If the perimeter of $\Delta ABC$ is $18.6 \, cm$,then the perimeter of $\Delta PQR$ is $\ldots \ldots \ldots cm$.

$E$ is the mid-point of a median $AD$ of $\triangle ABC$ and $BE$ is produced to meet $AC$ at $F$. Show that $AF = \frac{1}{3} AC$.