Either a rhombus, a square, a parallelogram or a rectangle.
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A trapezium is a quadrilateral with two parallel lines.
I don't think this is possible. there is not a quadrilateral with these qualities. If it is a quadrilateral, it will automatically have parallel lines, but there is not one that has both. The closest one would be the trapezoid, with a set of parallel lines, but no right angle. The square and rectangle have two sets of parallel lines and 4 right angles.
A parallelogram is a quadrilateral in which each of two sets of opposite sides consists of two parallel lines (or for math purists I should say, parallel line segments).
It is called a Rhombus.
There are two sets of parallel lines in a rectangle, which is to say each of the two sides are parallel to each other.A rectangle has two set of parallel sides