Parallelograms

Parallelogram is a quadrilateral whose opposite sides are parallel and equal.

A rectangle, a rhombus and a square are considered as parallelograms.

A trapezoid is quadrilateral with exactly one pair of opposite sides being parallel. Hence, it is not a parallelogram.

You have learnt a few properties of parallelogram through measurement. Recall the properties of a parallelogram.

• Each pair of opposite sides are equal and parallel.

In the diagram,

Opposite sides: AB||DC and AD||BC

AB=DC and AD=BC

• Opposite angles are equal.

• Diagonals of a parallelogram bisect each other.

In the diagram, OD=OB and OA=OC

• Each diagonal divides the parallelogram into two congruent triangles.

The properties of a parallelogram understood through measurement can also be proved through logical steps. But, before that let us recall some names associated with pairs of sides and angles of a quadrilateral.

Opposite sides

• of a quadrilateral:

Two sides of a quadrilateral, which have no common point, are called opposite sides.

In the diagram, AB and DC is one pair of opposite sides.

AD and BC is the other pair of opposite sides.

Consecutive sides

• of a quadrilateral:

Two sides of a quadrilateral, which have a common end point, are called consecutive sides. In the diagram,

AB and BC is one pair of consecutive sides.

BC, CD; CD, DA; and DA, AB are the other three pairs of consecutive sides.

Opposite angles

• of a quadrilateral:

Two angles, which do not include a side in their intersection, are called the opposite angles of a quadrilateral.

Consecutive angles

• of a quadrilateral:

Two angles of a quadrilateral, which include a side in their intersection, are called consecutive angles.