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Yes all rectangles are parallelogram but all parallelogram cannot be rectangles.
A parallelogram where all sides are equal is a square.
Yes.A parallelogram with all congruent sides is called a rhombus. A square is technically a parallelogram with all congruent sides as well.
A rhombus is a parallelogram, but a parallelogram isn't always a rhombus. A rhombus is a parallelogram where all the lines are the same length.