The quadrilaterals are those which are four sided closed figures. The quadrilaterals can be classified into different types according to their properties. It is very important to know the properties of each quadrilateral as it is very much useful to design the given place or land in the required form. We have already seen the fountains at the center of a definite shaped grass land in a park. Also while fixing tiles of definite shape in a given area we should know the properties of the quadrilaterals to make our job easier. In this section let us see the types of quadrilaterals, their properties and few problems based on quadrilaterals.

Parallelogram: A parallelogram is a quadrilateral whose pair opposite sides are parallel.

Properties of a Parallelogram:

1. Opposite sides are Congruent.
In the above parallelogram //gm LANE, LA = EN and AN = LE

2. Opposite sides are parallel.
LA // EN and AN // LE

3. Pair of adjacent angles are supplementary
$\angle L$ + $\angle A$ = 180o
$\angle A$ + $\angle N$ = 180o
$\angle N$ + $\angle E$ = 180o
$\angle E$ + $\angle L$ = 180o

4. Opposite Angles are Congruent.
$\angle L$ = $\angle N$
and $\angle E$ = $\angle A$

5. Diagonals bisect each other.
AO = OE and LO = ON

6. Each diagonal divides the parallelogram into pair of congruent triangles.
$\Delta LAN$ $\cong$ $\Delta NEL$
and $\Delta ALE$ $\cong$ $\Delta ENA$
→ Read More