Question

which statement can be used to prove that a given parallelogram is a rectangle?
the consecutive angles of the parallelogram are supplementary.
all the sides of the parallelogram are equal in measure.
the diagonals of the parallelogram are perpendicular.
the diagonals of the parallelograms are congruent.

Explanation:

• For a parallelogram, consecutive angles are always supplementary (by the property of parallelograms), so this does not prove it is a rectangle.
• If all sides of a parallelogram are equal, it is a rhombus, not necessarily a rectangle.
• If diagonals of a parallelogram are perpendicular, it is a rhombus.
• One of the properties of a rectangle (which is a type of parallelogram) is that its diagonals are congruent.

Answer:

The diagonals of the parallelograms are congruent.