Which polygon has diagonals that are congruent and are perpendicular bisectors of each other?

A square is a special type of rectangle and a rhombus, characterized by its properties of having all sides equal in length and all angles measuring 90 degrees. In a square, the diagonals have several unique characteristics: they are congruent (meaning they are of equal length) and they bisect each other at right angles (perpendicular). This means that not only do the diagonals split the square into equal triangles, but they also intersect each other at an angle of 90 degrees.

In contrast to the square, while a rectangle has congruent diagonals, they do not intersect perpendicularly. A rhombus has diagonals that are perpendicular to each other; however, these diagonals are not necessarily equal in length. A trapezoid generally does not possess diagonals that share such consistent properties. Therefore, the square stands out as the only polygon that meets the criteria of having diagonals that are both congruent and perpendicular bisectors of each other.