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.

A parallelogram is a simple quadrilateral and has 2 pairs of parallel sides. The opposite-facing are of equal length. The opposite-facing angles are of equal measure.

The diagonals bisect each other and divide the parallelogram into two equal parts. The consecutive angles are supplementary, Hence the diagonals of the parallelograms are congruent. This option D is correct.

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To prove that a given parallelogram is a rectangle, the diagonals of the parallelogram must be congruent.

Explanation:

Let us consider each statement to check and analyse as follows:

The consecutive angles of the parallelogram are supplementary. Supplementary angles are those whose sum of the angles is 180°. In a parallelogram, this is true but each angle is not a right angle to become a rectangle. All the sides of the "parallelogram are equal in measure". All the sides of the parallelogram are equal in measure which is same as in a rectangle but this statement alone cannot conclude the figure to be a rectangle. The diagonals of the "parallelogram" are perpendicular. The diagonals of the square and the parallelogram are perpendicular but this statement alone cannot conclude the figure to be a rectangle. The diagonals of the parallelogram are congruent. Congruent implies equality in all respects, identical in form, "coinciding" exactly when superimposed. The diagonals are congruent implies they are "equal in all respects" which resembles a rectangle.

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