Question

Which of the following statements must be true about a rectangle?

A)The opposite angles of a rectangle are complementary.


B)The diagonals of a rectangle are perpendicular.


C) The diagonals of a rectangle are congruent.


D)The consecutive sides of a rectangle are parallel.

Answer 1

C) The diagonals of a rectangle are congruent.

Explanation:

Complementary angles are defined as a pair of angles whose measures add up to 90°. Therefore, since the interior angles of a rectangle are always 90°, the opposite angles in a rectangle cannot be considered complementary; instead, they are supplementary, meaning their measures add up to 180°.

The diagonals of a rectangle are congruent in length and bisect each other. They are not usually perpendicular. When the diagonals are perpendicular, the rectangle transforms into a square.

Consecutive sides are sides of a polygon that are adjacent or next to each other, sharing a common vertex. In a rectangle, only its opposite sides are parallel, since all interior angles are right angles. Therefore, consecutive sides of a rectangle cannot be parallel.

So, the following statement is true about a rectangle:

• C) The diagonals of a rectangle are congruent.