State whether the statements are True or False.

(i) Every parallelogram is a trapezium ( )

(ii) All parallelograms are quadrilaterals ( )

(iii) All trapeziums are parallelograms ( )

(iv) A square is a rhombus ( )

(v) Every rhombus is a square ( )

(vi) All parallelograms are rectangles ( )

(i) [True]

⇒ The trapezium has a property

One pair of opposite sides are parallel

This is conveyed by parallelogram

as they have 2 pair of parallel sides

∴ Every parallelogram is a trapezium

(ii) [True]

⇒ The quadrilateral is known as

Polygon having four sides

This is conveyed by parallelogram

as they are also four sided polygon.

∴ Every parallelogram is a Quadrilateral

(iii) [False]

⇒ The parallelogram has a property

Both pair of opposite sides are parallel and equal

Which is not conveyed by trapezium

as they have only 1 pair of parallel sides

∴ Every trapezium is not parallelogram

(iv) [True]

⇒ The Rhombus has a property

Diagonal of rhombus bisect each other at 90°

This is conveyed by square

as their diagonal also bisect each other at 90°

∴ A square is a rhombus

(v) [False]

⇒ The square has a property

All angles of square are equal and 90°

And diagonals are equal and perpendicular bisector to each

other

Which is not conveyed by Rhombus

as their diagonal are perpendicular bisector but not equal

And their angles are also not equal to 90°

∴ Every rhombus is not a square.

(vi) [False]

⇒ The rectangle has a property

Every angle of rectangle is 90°

Which is not conveyed by parallelogram

as it have only opposite side angles are equal not 90°

∴ Every parallelogram are not rectangle.