What quadrilateral does not always have congruent diagonals?

A quadrilateral that does not always have congruent diagonals is a trapezoid. In a trapezoid, which has at least one pair of parallel sides, the diagonals are generally not congruent unless it is an isosceles trapezoid. Other types of trapezoids can have diagonals of different lengths. Thus, congruent diagonals are not a defining characteristic of all trapezoids.