Opposite angles of a quadrilateral $ABCD$ are equal. If $AB = 4 \, cm$,determine $CD$ (in $cm$).

Diagonals of a parallelogram are perpendicular to each other. Is this statement true? Give reason for your answer.

In $\Delta ABC$,$P$,$Q$,and $R$ are the midpoints of $AB$,$BC$,and $CA$ respectively. If $AB = 8 \text{ cm}$,$BC = 6.6 \text{ cm}$,and $CA = 5.4 \text{ cm}$,then find the perimeter of $\Delta PQR$ in $\text{cm}$. (in $.0$)

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 $BC = \frac{1}{2} QR$.

In parallelogram $PQRS$,diagonal $PR$ bisects $\angle P$. Prove that diagonal $PR$ bisects $\angle R$ also and $PQRS$ is a rhombus.

$P, Q, R$ and $S$ are respectively the mid-points of the sides $AB, BC, CD$ and $DA$ of a quadrilateral $ABCD$ in which $AC = BD$. Prove that $PQRS$ is a rhombus.