Question

which statement can be used to prove that a given parallelogram is a rectangle?

the opposite angles of the parallelogram are congruent.

the opposite sides of the parallelogram are congruent.

the diagonals of the parallelogram bisect the angles.

the diagonals of the parallelogram are congruent.

Explanation:

To determine which statement proves a parallelogram is a rectangle, recall properties:

• Opposite angles congruent and opposite sides congruent are true for all parallelograms, not just rectangles.
• Diagonals bisecting angles is a property of rhombuses, not rectangles.
• A key property of rectangles (a type of parallelogram) is that their diagonals are congruent. So the statement "The diagonals of the parallelogram are congruent" is the correct condition.

Answer:

The diagonals of the parallelogram are congruent. (The last option: "The diagonals of the parallelogram are congruent.")