Difficulty: Medium

Average Score: 69%

If a quadrilateral is a rectangle, which of the following statements must be true? Select ALL that apply.

Rationale

The quadrilateral has four congruent angles, two pairs of parallel sides, and the two diagonals have equal length.

A rectangle is defined as a quadrilateral with four right angles, which means it inherently has four congruent angles. Additionally, rectangles have two pairs of parallel sides and the property that both diagonals are equal in length.

A (The quadrilateral has four congruent sides.) YOUR ANSWER

While a rectangle does have four sides, they are not necessarily congruent. This characteristic is specific to a square, which is a special type of rectangle. Therefore, not all rectangles can be said to have four congruent sides.

B (The quadrilateral has four congruent angles.) CORRECT

This statement is true for rectangles, as all angles in a rectangle measure 90 degrees, making them congruent. This property is fundamental to the definition of rectangles.

C (The quadrilateral has two pairs of parallel sides.) CORRECT

Rectangles are defined as having two pairs of opposite sides that are parallel. This is a defining characteristic of all rectangles and is essential for their classification as quadrilaterals.

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

In rectangles, the diagonals are equal in length due to the congruence of the opposite angles and the parallel sides. This property holds true for all rectangles and is crucial for their geometric properties.

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

This statement is not true for rectangles. While the diagonals of a rectangle bisect each other, they are not necessarily perpendicular. This property is characteristic of rhombuses and squares, not rectangles.

Conclusion

In summary, a rectangle must possess four congruent angles, two pairs of parallel sides, and equal-length diagonals as essential properties. However, it does not necessarily have four congruent sides, nor are its diagonals perpendicular to one another. Understanding these properties helps differentiate rectangles from other quadrilaterals, such as squares and rhombuses.

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