Question

which of the following is a property of all rectangles?
a. the diagonals are perpendicular.
b. the diagonals bisect the vertex angles.
c. opposite sides are congruent.
d. only one pair of opposite sides is parallel.

Explanation:

Step1: Analyze option a

Diagonals of a rectangle are not perpendicular. Only in special cases like a square (a special rectangle) diagonals are perpendicular.

Step2: Analyze option b

Diagonals of a rectangle do not bisect the vertex angles. In a square (a special rectangle) diagonals bisect the vertex angles.

Step3: Analyze option c

By the definition of a rectangle (a parallelogram with four right - angles), in a parallelogram (and thus in a rectangle) opposite sides are congruent.

Step4: Analyze option d

In a rectangle, both pairs of opposite sides are parallel. It is a parallelogram property.

Answer:

C. Opposite sides are congruent.