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-they are both quadrilaterals
-paralleligram have 2 parallel sides while trapezoid has only 1 parallel side
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1)  four sides, four vertices
2)  The sum of interior angles is 360 degrees.
3)  with two diagonals that intersect each other

1)  Parallelogram has two pairs of opposite parallel sides; trapezoid has only one pair of opposite parallel sides.
2)  Parallelogram's diagonals are always congruent, trapezoids diagonals are sometimes congruent.
3)  The diagonals of parallelogram bisect each other; trapezoid's diagonals do not bisect each other.
4)  The opposite angles of parallelogram are always congruent; Trapezoid's opposite angles are never congruent.

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