They have four sides
They have four sides and four angles.
Quadrilateral shapes have four sides and four angles.
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yes
Like a closed 4-sided figure.
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.
Well, honey, let me break it down for you. All squares are indeed quadrilaterals, but not all quadrilaterals are squares. It's like saying all thumbs are fingers, but not all fingers are thumbs. So, yes, squares are a type of quadrilateral, but don't go thinking every four-sided shape is a square.
All quadrilaterals are polygons, but not all polygons are quadrilaterals.