It isn't really a square if it has no equal sides. A trapezoid can be drawn that has no equal sides, some can have two sides equal. Quadrilaterals include those 4-sided shapes with no sides equal but they also include all other 4-sided shapes. You would need to specify "Quadrilateral with no equal sides".
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Square
It may be a Rhombus or a Square
Yes it does - ALL four sides are equal in a square.
A square has 4 equal sides. And 4 ninety degree angles.
A square has four equal sides and four equal angles.