In a rectangle, which statement about diagonals is true?

In a rectangle, which statement about diagonals is true?

• A. The diagonals are equal in length.
• B. The diagonals are perpendicular.
• C. The diagonals are parallel.
• D. One diagonal is longer than the other.

Answer: (A)

The key idea is that opposite corners of a rectangle are connected by diagonals that have the same length. If the rectangle has side lengths a and b, each diagonal spans those same two dimensions, so its length is sqrt(a^2 + b^2) by the Pythagorean theorem. Since both diagonals connect opposite corners, they share this same distance and are equal in length.

They aren’t perpendicular in a rectangle (that special property occurs only in a square or certain rhombi), and they aren’t parallel because they cross each other at the rectangle’s center. Also, one diagonal isn’t longer than the other—their lengths are identical.