Question 32

A rectangle must have four congruent angles, two pairs of parallel sides, and equal-length diagonals.

In a rectangle, it is true that the quadrilateral has four congruent angles (each measuring 90 degrees), two pairs of parallel sides, and the diagonals are of equal length.

A) The quadrilateral has four congruent sides.

This statement is incorrect because, while a square (which is a special type of rectangle) has four congruent sides, a rectangle does not require this. A rectangle can have two pairs of sides that are equal in length but not all four sides congruent.

B) The quadrilateral has four congruent angles.

This statement is correct. By definition, a rectangle has four right angles, which are equal, meaning all angles are congruent.

C) The quadrilateral has two pairs of parallel sides.

This statement is also correct. A rectangle is defined by having two sets of opposite sides that are parallel, which is a fundamental characteristic of all rectangles.

D) The two diagonals of the quadrilateral have equal length.

This statement is correct as well. In a rectangle, the diagonals are equal in length, which distinguishes rectangles from other quadrilaterals that do not have this property.

E) The two diagonals of the quadrilateral are perpendicular to each other.

This statement is incorrect because, in a rectangle, the diagonals are not perpendicular. This property is true for rhombuses and squares, but not for all rectangles.

Conclusion

The correct statements concerning a rectangle are that it has four congruent angles, two pairs of parallel sides, and equal-length diagonals. The incorrect options fail to accurately describe the properties of a rectangle, as they either misrepresent its sides or the relationship between its diagonals. Thus, understanding these properties is crucial for accurately identifying and classifying rectangles in geometry.