This sounds like a kite, but the wording of the question is not clear. Disjoint and consecutive do not seem to go together.
A kite has a pair of congruent sides, which are adjacent, and another pair of congruent sides, which are adjacent.
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A kite is a quadrilateral in which two disjoints pairs of consecutive sides are congruent
a rhombus
A quadrilateral with congruent pairs of adjacent sides and no parallel sides is a kite.
4 sides
* both pairs of opposite sides are parallel * both pairs of opposite sides are congruent * both pairs of opposite angles are congruent * one pair of opposite sides are parallel and congruent * both diagonals bisect each other * all consecutive angle pairs are supplementary