# Which statement describes a parallelogram that must be a square?

## a) A parallelogram with diagonals that are congruent and opposite sides that are congruent

## b) A parallelogram with diagonals that bisect each other and opposite sides that are congruent

## c) A parallelogram with diagonals that are congruent and perpendicular

## d) A parallelogram with perpendicular diagonals

A square is a** **closed two-dimensional figure with four equal sides and four corners

## Answer: Option c- A parallelogram with diagonals that are congruent and perpendicular must be a square

Let us see how we arrived at this conclusion.

## Explanation:

The properties of a square are as follows

- All the sides of a square are congruent.
- All the angles in a square are right angles.
- Both pairs of opposite sides are parallel to each other.
- The diagonals are congruent, the diagonals are perpendicular to each other the diagonals also bisect each other.
- A square is a special kind of parallelogram whose all angles and sides are equal and congruent.

So, a parallelogram with a pair of congruent consecutive sides and diagonals that are congruent must have equal interior angles that is equal to a right angle and all equal sides for it to be a squar

Option A: A parallelogram with diagonals that are congruent and opposite sides that are congruent

This talks about only opposite sides being congruent which does not prove it's a square

Option B:A parallelogram with diagonals that bisect each other and opposite sides that are congruent

This doesn't talks about all four sides being congruent or diagonals being congruent hence,cannot say it is a square

Option C: A parallelogram with diagonals that are congruent and perpendicular

This talks about diagonals being congruent and perpendicular which proves that it is a square. Congruent diagonals are also a property of a rectangle

Option D: A parallelogram with perpendicular diagonals

Not enough information is given about the diagonals or sides being congruent hence, cannot say it's a square