[latexpage]

A Parallelogram is a quadrilateral with two pairs of parallel sides.

**Special Cases Of Parallelogram:**

**Rectangle** – A parallelogram with each angle equal to 90.

**Rhombus** – A parallelogram with four sides of equal length.

**Square** – A parallelogram with four sides of equal length and each angle being right angle.

**Characteristics of Parallelogram : **

**1.) Two pairs of opposite sides are equal in length.**

i.e. Here , in the above figure , Length of AB = Length of CD and Length of AD = Length of BC.

**2.)Two pairs of opposite angles are equal in measure.**

i.e. Here , in the above figure , <A = <C and <B = <D

**3.)** **Adjacent angles are supplementary.**

i.e. Supplementary means the sum of angles being equal to 180.

Here , in the above figure , <A+ < B = <B + <C = <C + <D = <D + <A = 180

**4.) Each diagonal divides the quadrilateral into two congruent triangles.**

Diagonal AC will divide the Parallelogram in two triangles ,$\triangle ADC$ and $\triangle ABC$ and both will be Congruent to each Other.

Similarly , Diagonal BD will divide the Parallelogram in two triangles ,$\triangle ADB$ and $\triangle CDB$ and both will be Congruent to each Other.

**5.)** **The sum of the squares of the sides equals the sum of the squares of the diagonals.**

${ AB }^{ 2 }+{ BC }^{ 2 }+{ CD }^{ 2 }+{ DA }^{ 2 }={ AC }^{ 2 }+{ BD }^{ 2 }$

**6.)The sum of the distances from any interior point to the sides is independent of the location of the point.**

**AREA OF PARALLELOGRAM : **

Area of a Parallelogram = Base X Height.

Area of Parallelogram is also equal to the sum of the two triangles made by the any one of the Diagonals.