Question

which statement can be used to prove that a given parallelogram is a rectangle?
the diagonals of the parallelogram are congruent.
the opposite sides of the parallelogram are congruent.
the diagonals of the parallelogram bisect the angles.
the opposite angles of the parallelogram are congruent.

Explanation:

To determine which statement proves a parallelogram is a rectangle, we analyze each option:

• "The opposite sides of the parallelogram are congruent": This is a property of all parallelograms, not unique to rectangles.
• "The diagonals of the parallelogram bisect the angles": This is a property of rhombuses, not a defining property of rectangles.
• "The opposite angles of the parallelogram are congruent": This is true for all parallelograms, not specific to rectangles.
• "The diagonals of the parallelogram are congruent": A key theorem states that if the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

Answer:

A. The diagonals of the parallelogram are congruent.