A quadrilateral always has four sides.
A square always has four sides
→ a square is always a quadrilateral.
A quadrilateral's only distinguishing feature is a shape with four sides.
A square has four sides, but also those four sides must all be the same length and all the angles are the same, at 90o.
So squares are always quadrilaterals, but quadrilaterals are only sometimes squares.
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-- A parallelogram is always a quadrilateral. -- A quadrilateral is sometimes a parallelogram.
A kite is always a quadrilateral because it has 4 sides
A rectangle is always a 4 sided polygon known as a quadrilateral.
A rhombus is sometimes a square but a square is always a rhombus. A square is a rhombus with all angles equal to 90 degrees.
A rhombus does not have right angles. A square always has right angles.