They are both 4 sided quadrilaterals.
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A kite is never a square but they are both 4 sided quadrilaterals
A kite is a quadrilateral is a kite if it has two sets of sides that are the same length and are adjacent to each other. A square fits this definition, so a square is a kite.
A kite, a rhombus (special case of a kite), a square (a special case of rhombus).
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