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No, a parallelogram is not another kind of quadrilateral.

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Q: Is a parallelogram any other kind of quadrilateral?

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Yes. A quadrilateral is any plane figure bounded by four straight lines. A parallelogram has both pairs of opposite sides parallel and is therefore a special kind of quadrilateral.

Any quadrilateral that is not a parallelogram can have only one diagonal that is bisected by the other.

Yes, it is.

You can have a trapezium, a kite or an arrowhead with right angled vertices, as well as a completely irregular quadrilateral. In fact, any kind of quadrilateral other than a parallelogram (or rhombus) can have a right angled vertex.

No, because a parallelogram is always a 4 sided quadrilateral.

All parallelograms are quadrilaterals. Not all quadrilaterals are parallelograms. A quadrilateral refers to any polygon with four sides. A parallelogram refers to any quadrilateral with two pairs of parallel sides.

No because any 4 sided shape is a quadrilateral which includes a parallelogram.

Any 4 sided polygon is a quadrilateral. The square, rectangle, rhombus, trapezoid and parallelogram are special cases of the quadrilateral. Any other 4 sided polygon is an irregular quadrilateral.

No reason at all. They could just as easily be in any other configuration.

A square, rectangle, rhombus, parallelogram, trapezium, kite and arrowhead will tessellate. Other quadrilaterals will not.

Yes

A quadrilateral is a parallelogram if and only if its diagonals bisect each other (this should be in any geometry book)