a quadrilateral is a shape with four equal sides.
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an iscoceles triangle
I don't think there's any special name for this.
It is a parallelogramIf one of the angles is a right angle (then they all are) and the quadrilateral is a rectangle.If both pairs of sides are equal in length (but none of the angles is a right angle) the quadrilateral is a rhombus.If the sides are equal and one of the angles is a right angle, the quadrilateral is a square.
If a quadrilateral has two pairs of opposite congruent sides, then the quadrilateral is a parallelogram.
A kite has two pairs of equal sides with no parallel sides.