Yes.
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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.
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Trapezoids. All other quadrilaterals either have two pairs of parallel sides or none.
Yes, all trapezoids must have one pair of congruent sides.
No. All trapezoids have only one pair of parallel sides which are different in length. In an isosceles trapezoid the lengths of the two non-parallel sides are equal.