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The different quadrilaterals drawn below:

Observe that :

⦁ One pair of opposite sides of quadrilateral ABCD in Fig. (i) namely, AB and CD are parallel. You know that it is called a trapezium.

⦁ Both pairs of opposite sides of quadrilaterals given in Fig. (ii), (iii) , (iv) and (v) are parallel. Recall that such quadrilaterals are called parallelograms.

⦁ In parallelogram MNRS of Fig. (iii), note that one of its angles namely ∠ M is a right angle. It is called a rectangle.

⦁ The parallelogram DEFG of Fig. (iv) has all sides equal and we know that it is called a rhombus.

⦁ The parallelogram ABCD of Fig. (v) has ∠ A = 90° and all sides equal; it is called a square.

⦁ In quadrilateral ABCD of Fig. (vi), AD = CD and AB = CB i.e., two pairs of adjacent sides are equal. It is not a parallelogram. It is called a kite.

Note that a square, rectangle and rhombus are all parallelograms.

⦁ A square is a rectangle and also a rhombus.

⦁ A parallelogram is a trapezium.

⦁ A kite is not a parallelogram.

⦁ A trapezium is not a parallelogram (as only one pair of opposite sides is parallel in a trapezium and we require both pairs to be parallel in a parallelogram).

⦁ A rectangle or a rhombus is not a square.