Which description does not guarantee that a quadrilateral is a square?

Solution:

A square is a closed two-dimensional figure with four equal sides and four right angles.

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 congruent.

A rectangle and a rhombus are also parallelograms with perpendicular diagonals. Similarly, the description of a quadrilateral with four equal sides can also mean a rhombus or a square.

Hence, the description of a parallelogram with perpendicular diagonals does not guarantee that the quadrilateral is a square.

Which description does not guarantee that a quadrilateral is a square?

Summary:

A parallelogram with perpendicular diagonals can be a square, a rectangle, or a rhombus. Hence, this description does not guarantee that the quadrilateral is a square.