Yes they can definitly be similar.
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A rectangle with four equal sides would not be a rectangle, it would be a square. In a rectangle opposite sides are equal in length and are parallel.
parallel sides, four right angles, quadrilateral
A rectangle has four right angles but is not a square.
A rectangle is a quadrilateral with four right angles True (Apex)
A square is a special case of a rectangle. Every square is a rectangle, but not every rectangle is a square. A square is a rectangle with four sides that are all equal in length.