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Yes. Those trapezoids with four right angles are called squares. Since in order to be a trapezoids, a shape must be a quadrilateral with with one set of parallel lines, and a square fits those requirements. In conclusion, the trapezoids that have four right angles are squares.
By cutting through its diagonal and cutting off each corner parallel to its diagonal which will leave you with 2 triangles and 2 trapezoids.
a trapezoid requires at least two parallel sides, so a square is a special case of trapezoid, but not all trapezoids are square.
The main difference between squares and trapezoids is that, while the length all four sides of a square are equal, trapezoids have two sides with equal length and two sides of different length. Also, the opposite pairs of sides in a square are parallel, while only one pair of sides in a trapezoid is parallel.