Let the parallelogram be ABCD and AC and BD are its diagonals
In ΔADC and ΔBCD
AD=BC(opp. sides of a parallelogram are equal)
∴By SSS congruence rule
ΔADC is congruent to ΔBCD
Since in a parallelogram adjacent angles are supplementary
and since ∠ADC=∠BCD
since in a parallelogram adjacent angles are 90°, the parallelogram is a rectangle.