In $\Delta XYZ$,$A, B$ and $C$ are the midpoints of $XY, YZ$ and $XZ$ respectively. If $AB = 5.2\, cm$,$BC = 4.3\, cm$ and $AC = 6.5\, cm$,then find the perimeter of $\Delta XYZ$ in $cm$.

In quadrilateral $ABCD$,$\angle A : \angle B : \angle C : \angle D = 1 : 4 : 2 : 2$. Find the measure of each angle of the quadrilateral.

All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?

Points $P$ and $Q$ have been taken on opposite sides $AB$ and $CD$ respectively of a parallelogram $ABCD$ such that $AP = CQ$ (see figure). Show that $AC$ and $PQ$ bisect each other.

$PQ$ 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.

Can all the four angles of a quadrilateral be obtuse angles? Give reason for your answer.