Home » CAT Questions » Parallelogram

Parallelogram

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.


Leave a comment