Question

which characteristic guarantees that a parallelogram is a rectangle?
all of the sides are congruent.
the opposite sides are parallel.
the diagonals are perpendicular bisectors.
the diagonals are congruent.

Explanation:

• Option 1: All sides congruent makes it a rhombus (a type of parallelogram), not necessarily a rectangle.
• Option 2: Opposite sides parallel is a property of all parallelograms, not just rectangles.
• Option 3: Diagonals being perpendicular bisectors makes it a rhombus.
• Option 4: In a parallelogram, if the diagonals are congruent, then it is a rectangle. This is a theorem in geometry.

Answer:

The diagonals are congruent.