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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.
Yes, if it is an equiangular or equiangular and equilateral parallelogram (rectangle or square).
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.
The terms equiangular means a polygon having the same angle between any two adjacent sides. Equilateral means all sides of equal length. A polygon can be equilateral without being equiangular (the rhombus) and equiangular without being equilateral (the rectangle). If a polygon is both equilateral and equiangular, it is a "regular polygon" such as the pentagon, square, and equilateral triangle.
No, an equilateral triangle has to be equiangular, but an equiangular triangle does NOT have to be equilateral