Which statement is true about isosceles trapezoids?

An isosceles trapezoid is defined as a trapezoid where the non-parallel sides, known as the legs, are of equal length, and importantly, the base angles are congruent. This means that the angles adjacent to each base are equal. This property arises from the symmetry of the isosceles trapezoid, making it a distinctive feature that helps in identifying it among other types of trapezoids.

In an isosceles trapezoid, since the legs are of equal length and the bases are parallel, the angles at each end of the legs have to be equal in measure. Thus, stating that the base angles are congruent accurately reflects a fundamental property of isosceles trapezoids, supporting the assertion that option C is true.

The other statements do not hold true for isosceles trapezoids: not all sides can be of distinct lengths since the legs must be equal, diagonals are indeed congruent in isosceles trapezoids, and by definition, they do have a pair of parallel sides. Therefore, the statement regarding the congruency of base angles stands out as the correct and defining characteristic of isosceles trapezoids.