No. A trapezoid does not necessarily have any symmetry.
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A trapezoid has one line of symmetry.
Only if it is in the form of an isosceles trapezoid
Not normally but an isosceles trapezoid does.
A trapezium does not have rotational symmetry.
If it is an isosceles trapezoid, then there is only one line of symmetry, right down the middle of it from top to bottom. If it is a plain old trapezoid with no congruent sides, then there are no lines of symmetry.