A rectangle is not always equilateral. A square and a rhombus both have four equal sides.
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A rectangle is not always equilateral, although it is always equiangular. A rhombus is not always equiangular, but is always equilateral. A square is both equilateral and equiangular.
A rhombus cannot be a square. A rectangle is an equiangular parallelogram. A rhombus is an equilateral parallelogram. A square is an equilateral and equiangular parallelogram. Thus, a square is both a rectangle and a rhombus.
A rectangle is sometimes a square, but not always. When it is, it's also a rhombus. A rhombus is sometimes a square, but not always. When it is, it's also a rectangle. A square is always a rhombus and always a rectangle. Rectangles, rhombera, and squares are always parallelograms and quadrilaterals.
A square is a rectangle, a rhombus, an equilateral parallelogram, and a regular quadrilateral.
A rhombus and its variant (a square).