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No. A trapezoid is defined as a quadrilateral with two parallel sides. Therefore, the quality of quadrilateral is necessary, and this condition is satisfied. ... Any other shape can have four sides, but if it does not have (at least) two parallel sides, it cannot be a trapezoid.
It is an inscribed quadrilateral or cyclic quadrilateral.
It is simply a quadrilateral - there is no special name for such a quadrilateral.
It is an arrowhead quadrilateral
There is no specific name for such a quadrilateral.