The Mid-Point Theorem

In the given figure, $ABCD$ is a parallelogram in which $P$is the mid-point of $DC$ and $Q$is a point on $AC$ such that $CQ=\frac{1}{4}AC$and $PQ$product meet $BC$ at $R$, then,

In a given figures, if $ABCD$ is a rectangle and $P,Q$ are the mid-points of $AD,DC$ respectively. Then, the ratio of lengths $PQ$ and $AC$ is equal to

$D$ And $E$ are the mid-points of the sides $AB$ and $AC$, respectively of $△ABC$. $DE$ is produced to $F.$ To Prove that $CF$ is equal and parallel to $DA,$we need an additional information which is-

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

In a $△ABC$, $P$, $Q$ and $R$ are the mid-points of sides $BC$, $CA$ and $AB$ respectively. If $\mathrm{AB}=21 \mathrm{cm}$, $\mathrm{BC}=29 \mathrm{cm}$ and $\mathrm{AB}=30 \mathrm{cm}$. The perimeter of the quadrilateral $ARPQ$ is $\_\_\_\_\_\_\_\_\_\_\_\_\_\_$.