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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.
No
No, trapezoids are not rectangles. While both shapes have four sides, rectangles have opposite sides that are equal in length and all interior angles are right angles, whereas trapezoids have only one pair of opposite sides that are parallel.
Certain quadrilaterals have right angles. Right trapezoids are the most general example. Rectangles are specialized right trapezoids, and squares are specialized rectangles. There may be more but I can't recall them. Many rhombuses and parallelograms have no right angles. However, they might (and then you'd probably call them squares or rectangles but they are also technically rhombuses, parallelograms and trapezoids).
As trapezoid is a quadrilateral. All quadrilaterals have 4 angles along with 4 sides