All quadrilaterals are not parallelograms. A quadrilateral is a closed 2D shape having four vertices. It is called a parallelogram when its opposite sides are parallel to each other. Examples of quadrilaterals that are not parallelograms are trapezoids, kite and irregular quadrilaterals. Squares, rectangles and rhombus are the quadrilaterals that are parallelograms.

...No, a quadrilateral is any shape with four sides and a parallelograms is when opposite sides are parallel and equal in length, and opposite angles are equal.

For example, a square, rectangle, or rhombus are parallelograms.

A trapezoid is NOT a parallelogram, but it's a quadrilateral.

Not all quadrilaterals are parallelograms.

It doesn't work both ways, all parallelograms are quadrilaterals but not all quadrilaterals are parallelograms seeing as we have irregular quadrilaterals.

A quadrilateral is just a polygon with 4 sides hence the use of prefix quad.

The answer to this is no. A parallelogram has two pairs of parallel sides. Therefore, if you had a kite shape then this would not be a quadrilateral as a kite doesn't have any parallel sides.

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