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.