It is given that ABCD is a parallelogram. So opposite sides of ABCD are equal and parallel to each other, which means,
[tex]DA\cong CB\text{ and }DC\cong AB[/tex]
The diagonal of a parallelogram bisect each other. If diagonal of parallelogram are equal to each other then parallelogram is a rectangle. So sufficient condition for a parallelogram ABCD to be a rectangle is,
[tex]DE\cong AE[/tex]
So parallelogram ABCD is rectangle if DE is equal to AE, as diagonal of rectangle are equal to each other.
