A trapezoid can be proven isosceles by proving that the 2 legs are congruent (by definition), or that the 2 base angles (either upper or lower) are congruent.

Yes, the diagonals of a trapezoid are congruent. Another Answer:- The diagonals of a trapezoid are congruent only when it is in the form of an isosceles trapezoid.

The only real characteristic of a trapezoid is that one pair of opposite sides is parallel. For an isosceles trapezoid, in addition to one pair of opposite sides being parallel; the legs are congruent; each pair of base angles is congruent; and the diagonals are congruent.