In $\Delta ABC$,$P$ and $Q$ are the midpoints of $AB$ and $AC$ respectively. If $BC = 8.2 \text{ cm}$,then $PQ = \dots \text{ cm}$.

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.

$P, Q, R$ and $S$ are respectively the mid-points of the sides $AB, BC, CD$ and $DA$ of a quadrilateral $ABCD$ such that $AC \perp BD$. Prove that $PQRS$ is a rectangle.

In $\Delta ABC$,$X$ and $Y$ are the midpoints of $AB$ and $AC$ respectively. State the type of quadrilateral $XBCY$.

The quadrilateral formed by joining the mid-points of the sides of a quadrilateral $PQRS,$ taken in order,is a rhombus,if

One angle of a quadrilateral is $108^{\circ}$ and the remaining three angles are equal. Find each of the three equal angles. (in $^{\circ}$)