This statement is true. A rectangle is a specific type of parallelogram where all angles are right angles, and the diagonals are congruent. If a parallelogram does not have congruent diagonals, it cannot be a rectangle.
Here’s why:
- In a rectangle, the diagonals are always equal in length. This is a defining property of rectangles.
- If a parallelogram has diagonals that are not congruent, it means that the figure does not meet the criteria for being a rectangle.
- Therefore, if a parallelogram lacks congruent diagonals, it cannot be classified as a rectangle.
In summary, the statement is true because congruent diagonals are a necessary condition for a parallelogram to be a rectangle.