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If a set of equal sides are adjacent, then the quadrilateral is a "kite" shape. If a set of equal sides are opposite, then the quadrilateral is a parallelogram.
A trapezium or trapezoid.
trapzoid
Only if it is a trapezoid (US usage) with one set of parallel sides, or a parallelogram with both sets of opposite sides parallel. The term quadrilateral only means that the shape has 4 sides.
It could easily be taken for a trapezoid.