Parallelogram:Its Properties and Formulas

 

Properties of a Parallelogram

1. The opposite sides of a parallelogram are equal; AB = DC & AD = BC.
2. The opposite angles of a parallelogram are equal; $\angle A=\angle C\And \angle B=\angle D$.
3. The diagonals of a parallelogram bisect each other; AO = CO & BO = DO.

Area of Parallelogram = Base $\times $ Height
                                   = DC $\times $ AE

Since opposite sides of parallelogram are equal. Therefore,
Perimeter of Parallelogram = $2\times (l+b)$ ; here $l$ and $b$ are the lengths of its two adjacent sides.

Conditions required to prove a quadrilateral to be a Parallelogram

1. A quadrilateral is a parallelogram, if its opposite sides are equal.
2. A quadrilateral is a parallelogram, if its opposite angles are equal.
3. A quadrilateral is a parallelogram, if it has one pair of opposite sides parallel and equal.
4. A quadrilateral is a parallelogram, if its diagonals bisect each other.



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