If it is a square or a rectangle, then yes, it will have lines of symmetry.
But if you're thinking of your typical parallelogram that does not have another name, then no, it does not have lines of symmetry.
Basically, no.
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Some people say a parallelogram does have a line of symmetry because it looks like a rhombus but the truth is that a parallelogram does not have a line of symmetry because if you take paper and fold it in any way in a shape of a parallelogram so a parallelogram does not have a line of symmetry
First of all to correct your spelling. It is 'parallelogram'. A parallelogram does NOT have any lines of symmetry, unless it is a rectangular paralleligram. Where upon it has two lines of symmetry, viz/ a vertical line through the centre and an horizontal line through the centre.
In general, no. Not unless the parallelogram has at least one right angle.
A trapezium can have either 0 or 1 line of symmetry, depending on its specific shape. If the trapezium is a parallelogram, it will have one line of symmetry, which is the line that divides the shape into two equal halves. However, if the trapezium is not a parallelogram, it will have no lines of symmetry, as there is no way to divide it into two equal halves through a single line.
parallelogram