Yes, all trapezoids must have one pair of congruent sides.
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No. Most trapezoids don't even have one pair of congruent sides. Only isosceles trapeoids have one pair; none have more than one pair.
By definition, all trapezoids must have one pair of parallel sides. Therefore, an isosceles has one pair of congruent angles.
they have to because if they didn't it would be some sort of pentagon. so... yes
Yes.
"It is a quadrilateral with exactly one pair of parallel sides." is the true one. Some people define it as having at least one pair of parallel sides, so if your teacher is one of those people then all of the answers are wrong, but since all of the other answers are definitely wrong then this is the only one that could be right.