Final answer:
a), the diagonals of a rectangle are always equal and bisect each other. They intersect at their midpoints, but they are not perpendicular to each other.
Step-by-step explanation:
The correct answer is option a which states that the diagonals of a rectangle are always equal and bisect each other. In a rectangle, not only are the opposite sides equal in length, but the diagonals are of equal length as well.
The diagonals of a rectangle also bisect each other, meaning they cut each other exactly in half at the point where they intersect. This property is true for all rectangles, and it is an important characteristic that helps differentiate rectangles from other quadrilaterals.
It's noteworthy that while the diagonals of a rectangle do bisect each other, they are not perpendicular; they do not form a 90° angle with each other. In a rectangle, the diagonals are congruent but maintain the angles of the corners from which they originate.
Therefore, options b, c, and d are incorrect as they incorrectly characterize the relationship between the diagonals of a rectangle.
A rectangle is a quadrilateral with opposite sides that are equal in length and four right angles. The diagonals of a rectangle always have two important properties: they are equal in length and they bisect each other.
For example, in a rectangle with sides AB and CD, the diagonal AC is equal in length to the diagonal BD. Additionally, the point where AC and BD intersect (point O) is the midpoint of both diagonals, meaning that it divides each diagonal into two equal halves.