no
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Not necessarily. Usually only the opposite side are of equal length. If all 4 sides are of the same length, the parallelogram is [also] called a rhombus.
Not necessarily; it is a parallelogram - a rectangle is a parallelogram in which all angles are 90o. It could also be a rhombus - a rhombus is a parallelogram with all lengths the same; a square is a rhombus in which all angles are 90o.
A rhombus is a special case of a parallelogram where all side are the same length.
A parallelogram is just a rectangle leaned to one side
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.