Question

the diagonals of a rectangle are equal. sometimes always never

Explanation:

Step1: Recall the properties of a rectangle

A rectangle is a quadrilateral with four right angles. Let \(ABCD\) be a rectangle with \(AB = CD\), \(AD=BC\), and \(\angle A=\angle B=\angle C=\angle D = 90^{\circ}\).

Step2: Use the Pythagorean theorem to find the length of the diagonals

For diagonal \(AC\), by the Pythagorean theorem \(AC^{2}=AB^{2}+BC^{2}\). For diagonal \(BD\), \(BD^{2}=AB^{2}+AD^{2}\). Since \(AD = BC\) (opposite sides of a rectangle are equal), we have \(AC^{2}=BD^{2}\), so \(AC = BD\).

Answer:

B. always