what is the rule for the quadrilaterals that the man is holding up?

and/or what is the rule for all the quadrilaterals that the woman is holding?

e.g. he is holding up shapes that have two interior obtuse angles

e.g. his rule is the shapes must have 2 pairs of parallel sides i.e. be parallelograms

e.g. her rule is that the shapes do not have exactly one line of symmetry

e.g. his rule is that the shapes have 2 or more lines of symmetry

e.g. her rule is that the shape is a trapezium his rule is that the shapes have rotational symmetry order 2 or more

e.g. her rule is that the shapes have one or more pairs of parallel sides:

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