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Parallelogram

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

quad-parallelogram
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 : 

ParallelogramArea.svg

 

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.