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.
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A right angle trapezoid
Yes. Not here, of course, but it can be done. Draw a right angle. Draw two more lines from those end points at acute angles that connect in the middle. It will look something like a chevron, a "V" shape.
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.
It is nearly the shape of a square but one side is sloping and I think it is called a trapezoid
Right angle triangle, yup that's right