The diagonals of a quadrilateral ABCD are perpendicular. The quadrilateral formed by joining the mid points of its sides is known as _________.

From above figure,  $AC,BD$ are diagonals of quadrilateral  $ABCD$are perpendicular.

$Points P, Q, R, and S$ are mid-points of $AB$and  BC respectively.

In ΔABC , P and  Q are mid points of  AB  and  BC. So ,by Mid point theorem $\therefore PQ\parallel AC; PQ=\frac{1}{2}AC.........\left(1\right)$

Similarly in  $∆ACD , R$,  and $S$ are mid point of sides CD and AD.

$\therefore SR\parallel AC; SR=\frac{1}{2}AC.......\left(2\right)$

From (1) and (2). we get

$PQ\parallel SR$ and  $PQ\parallel SR$

Hence, PQRS is parallelogram  ( pair of opposite sides are equal and parallel)

Now, $RS\parallel AC$ and $QR\parallel BD$

Also, $AC\perp BD$ (Given)

$\therefore RS\perp QR$

Thus, PQRS is a rectangle.