A parallelogram is a four-sided shape with opposing sides being parallel. Therefore, a parallelogram may be a square, a rectangle, a rhombus (a sort of slanted square), or the shape most commonly referred to as a parallelogram is a sort of slanted rectangle. (Trapezoids are NOT parallelograms because only one pair of opposing sides are parallel)
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it is a 4 sided figure that can sometimes be mistaken as a rhombus
Yes. All rhombuses are parallelograms, but the reverse is not true. (I.e. there are parallelograms which are rhombuses and there a parallelograms that are not rhombuses. -- Just like Every bus has wheels but not everything with wheels is a bus.)
Not necessarily. All parallelograms are quadrilaterals but not all quadrilaterals are parallelograms. Parallelograms are more specific instances of quadrilaterals. Its like saying all squares are rectangles but not all rectangles are squares.
No. All rhombi (rhombuses) are parallelograms but all parallelograms are not rhombi.
No but all parallelograms are trapezoids