Question

ABCD is a quadrilateral and BD is one of its diagonals as shown in fig. Show that ABCD is a parallelogram and find its area.

Answer 1

Since diagonal BD intersects transversals AB and DC at B and D respectively such that
$\angle ABD=\angle CDB\text{[Each equal to}{90}^{\circ }]$
i.e. alternate interior angles are equal.
$\therefore AB||DC$
Also, AB = DC [Each equal to 5.2 cms (Given)]
Thus, one pair of opposite sides AB and DC of quadrilateral ABCD are equal and parallel.
Hence, ABCD is a parallelogram.
Now
$ar\left(ABCD\right)=Base\times \text{Corresponding altitude}$
$=AB\times BD=5.2\times 4=20.8{\text{cm}}^2$