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Yes, a trapezoid is a specific type of quadrilateral that has one pair of parallel sides. It does not have any other special name.
Square = parallelogram and a square trapezoid = trapezoid Parallelogram = Parallelogram
An isosceles trapezoid
The type of characteristics a trapezoid has or any other shape has makes it special in so many different ways
trapezoid
In general, trapezoids do not have right angles. In fact, a trapezoid with a right angle is a special case, called a rectangle.