Can a trapeziod ever be a rectangle?
No it cannot
The definition of a trapezoid is that it is a quadrilateral with exactly one pair of parallel sides. Rectangles and squares have two pairs of parallel lines. Using the idea of exactly one pair of parallel sides, the trapezoid cannot be a square or rectangle.
Some definitions of trapezoid (British trapezium) are exclusive, specifying that a trapezoid has exactly one pair of parallel sides.
Such definitions exclude parallelograms, rhombuses, rectangles or squares from being counted as trapezoids.
In my opinion, the more useful definitions of trapezoid are inclusive, specifying that a trapezoid is a quadrilateral with a pair of opposite sides that are parallel.
Under the inclusive definition, more specialised quadrilaterals including parallelograms, rhombuses, rectangles and squares are all special cases of trapezoid.
By Tomruen (Own work) [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons