Home » CAT Questions » Parallelogram

# Parallelogram

[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

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.