Question

Can diagonal of a parallelogram be congruent to one of its sides?

Explain your answer.

Answer 1

Parallelogram:

The diagonal of a parallelogram cannot be congruent to one of its sides.

A parallelogram has congruent and parallel opposite sides, while the diagonal of the parallelogram joins two opposite vertices or endpoints.

The diagonal of a parallelogram is always longer than the other sides, and cannot be congruent to any of the sides.

For example a square which is a parallelogram have side lengths of one unit each then its diagonal has a length of $\sqrt{2}units$ which shows side and diagonal can never be congruent for any given parallelogram

Hence, the diagonal of a parallelogram cannot be congruent to one of its sides.