Usually they do not, but in an isosceles trapezoid they do.
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No, the diagonals of a trapezoid do not necessarily bisect each other. Only in an isosceles trapezoid, where the two non-parallel sides are congruent, will the diagonals bisect each other. In a general trapezoid, the diagonals do not bisect each other.
No.
No.
False.
trapezoid