Yes, a shape is symmetrical if it can be cut in half in any way, and be the same on both sides.
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Symmetric is a term used to describe an object in size or shape. For example, you could say that an orange is symmetric to the sun or a glass is symmetric to a cone
They both have rotational symmetry - of order 2. But whereas a rectangle has 2 axes of symmetry, a parallelogram has none.
The shape descibed is not a symmetric figure. If it is folded on the diagonal line described, then the corners would stick off the sides. If the question is implying that they want to fold it in a differant way, then it would not be symmetrical because of the line. The line would not be in the place on both sides.
rectangle