To establish that a quadrilateral is a rectangle, which property must be demonstrated?

To establish that a quadrilateral is a rectangle, which property must be demonstrated?

• A. All sides are congruent
• B. Both pairs of opposite sides are congruent and diagonals are also congruent
• C. Only one pair of angles is complementary
• D. At least one angle is a right angle

Answer: (B)

To demonstrate that a quadrilateral is a rectangle, it is essential to show that both pairs of opposite sides are congruent and that the diagonals are also congruent. This is because a rectangle is defined not merely by having right angles but also by the properties that relate to its sides and diagonals. In a rectangle, the property of having both pairs of opposite sides equal ensures that the shape retains the characteristics of parallelograms, and congruent diagonals indicate that the figure must be equidistant and maintain the parallel properties necessary for right angles to occur. Whereas having just one pair of angles as complementary does not provide enough information to conclude that all angles are right angles, demonstrating congruency in both sides and diagonals confirms the quadrilateral has the essential characteristics of a rectangle: opposite angles are equal and diagonals bisect each other. Thus, showing both pairs of opposite sides are congruent and the diagonals are congruent provides the complete assurance needed to classify the shape as a rectangle.

To demonstrate that a quadrilateral is a rectangle, it is essential to show that both pairs of opposite sides are congruent and that the diagonals are also congruent. This is because a rectangle is defined not merely by having right angles but also by the properties that relate to its sides and diagonals.

In a rectangle, the property of having both pairs of opposite sides equal ensures that the shape retains the characteristics of parallelograms, and congruent diagonals indicate that the figure must be equidistant and maintain the parallel properties necessary for right angles to occur.

Whereas having just one pair of angles as complementary does not provide enough information to conclude that all angles are right angles, demonstrating congruency in both sides and diagonals confirms the quadrilateral has the essential characteristics of a rectangle: opposite angles are equal and diagonals bisect each other.

Thus, showing both pairs of opposite sides are congruent and the diagonals are congruent provides the complete assurance needed to classify the shape as a rectangle.