quadrilateral. not all, but it can. No, its obviously a trapizoid
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This is the definition of a trapezoid. Two parallel sides, and two non-parallel. ■
There is no generic name. Any polygon with 4 or more sides can have 2 parallel sides. There are also non-polygonal shapes that can have parallel sides: for example, a circle that is stretched out into a cigar shape can have two parallel sides.
In a general trapezium, the non-parallel sides are not congruent. However, in an isosceles trapezium, the non-parallel sides are congruent. So the shape is like an isosceles triangle with its apex chopped off by a straight line parallel to its base.
A regular hexagon (if you can use non-regular shapes then there's an infinite number)
A square, a rectangle, a rhombus and a parallelogram would all fit the given description