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)

Diagonals in a rectangle have the same length. If you label the rectangle’s width as w and height as h, each diagonal connects opposite corners and creates two right triangles with legs w and h. The length of each diagonal is sqrt(w^2 + h^2), so both diagonals are equal. The other statements don’t fit: diagonals cross each other rather than run parallel, and in a non-square rectangle they aren’t perpendicular; also neither diagonal is longer than the other because of the shape’s symmetry.

Diagonals in a rectangle have the same length. If you label the rectangle’s width as w and height as h, each diagonal connects opposite corners and creates two right triangles with legs w and h. The length of each diagonal is sqrt(w^2 + h^2), so both diagonals are equal. The other statements don’t fit: diagonals cross each other rather than run parallel, and in a non-square rectangle they aren’t perpendicular; also neither diagonal is longer than the other because of the shape’s symmetry.