No. Most trapezoids don't even have one pair of congruent sides.
Only isosceles trapeoids have one pair; none have more than one pair.
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Yes, all trapezoids must have one pair of congruent sides.
No. A trapezoid only has one pair of parallel sides.
Trapezoids have only one pair of parallel sides. A parallelogram has two pair of parallel sides.
By definition, all trapezoids must have one pair of parallel sides. Therefore, an isosceles has one pair of congruent angles.
No, trapezoids are not rectangles. While both shapes have four sides, rectangles have opposite sides that are equal in length and all interior angles are right angles, whereas trapezoids have only one pair of opposite sides that are parallel.