Which description does not guarantee that a quadrilateral is a square?
A square is a closed two-dimensional figure with four equal sides and four right angles.
Answer: 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.
Let us see how we arrived at this conclusion.
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.