In a rectangle, which statement about the diagonals is true?

In a rectangle, which statement about the diagonals is true?

• A. Diagonals are perpendicular.
• B. Diagonals are parallel.
• C. Diagonals do not intersect.
• D. Diagonals are equal in length.

Answer: (D)

In a rectangle, the diagonals have equal length. Imagine the rectangle has width w and height h. One diagonal forms a right triangle with legs w and h, so its length is sqrt(w^2 + h^2). The other diagonal also spans the same width and height, so it has the same length sqrt(w^2 + h^2). Thus both diagonals are equal in length. The diagonals are not perpendicular in a typical rectangle (that happens in special cases like a square). They do intersect at the center, but they are not parallel. The key point is their lengths are the same.

In a rectangle, the diagonals have equal length. Imagine the rectangle has width w and height h. One diagonal forms a right triangle with legs w and h, so its length is sqrt(w^2 + h^2). The other diagonal also spans the same width and height, so it has the same length sqrt(w^2 + h^2). Thus both diagonals are equal in length.

The diagonals are not perpendicular in a typical rectangle (that happens in special cases like a square). They do intersect at the center, but they are not parallel. The key point is their lengths are the same.