# 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 congruent and 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 congruent adjacent sides and diagonals that are congruent must have equal interior angles that are equal to right angles is a square.

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. It can be a rectangle as well.

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

This doesn't talk about all four sides being congruent or diagonals being congruent hence, cannot say it is a square. It can be a rhombus as well.

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.

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

### Hence, a parallelogram with diagonals that are congruent and perpendicular must be a square.

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