Not normally but if it's an isosceles trapezoid it will have a pair of congruent sides
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They can be as for example in an isosceles trapezoid.
A trapezoid with congruent diagonals is an isosceles trapezoid.
No, not all angles in a trapezoid are congruent. A trapezoid may have two pairs of congruent angles, or may have no congruent angles.
Only the diagonals of isosceles trapezoids are congruent.
A trapezoid, in general, does not have congruent sides.