Q: Are all Parallelogram quadrilaterals

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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.

A parallelogram has two diagonals the same as all 4 sided quadrilaterals

No but they are both 4 sided quadrilaterals.

No but they are both 4 sided quadrilaterals.

All 4 sided polygons are quadrilaterals such as a square, rectangle, parallelogram, rhombus, kite ... etc

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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, but all parallelograms are quadralaterals.

No, a trapezoid is not a parallelogram.

Parallelograms!

All four sided shapes are quadrilaterals which includes parallelograms.

square, rectangle, trapezoid, rhombus, parallelogram, kite, and irregular quadrilaterals

A parallelogram has two diagonals the same as all 4 sided quadrilaterals

All quadrilaterals have 4 sides such as a square, a rectangle, a rhombus, a parallelogram, a trapezoid, a trapezium and a kite.

No but they are both 4 sided quadrilaterals.

No but they are both 4 sided quadrilaterals.

A rectangle, a rhombus, a kite, a trapezoid and a parallelogram are all examples of quadrilaterals which are not square.

-- A parallelogram is always a quadrilateral. -- A quadrilateral is sometimes a parallelogram.