yes, but not necessarily a square
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quadrilateral quadrangle
A quadrangle or quadrilateral (a shape with 4 angles or 4 sides, respectively). Special names normally come in when you DO have special characteristics, not when you don't.
No, a quadrangle has four angles and four sides.
The figure, as described, is impossible. If a quadrangle has 2 pairs of parallel sides then the number of right angles can be 0 or 4, but not 2.
I think it is "quadrangle". If it has 4 equal sides and 4 right angles, "square" is right.