**Definition:** A quadrilateral is a figure closed by four line segments. The line segments are the sides of the quadrilateral.

**Or, A quadrilateral is a plane figure bounded by four straight .**

* Sum of four interior angles of a quadrilateral is 4 right angles or 3600.

Diagonal: The straight line which joins the opposite angular points in a quadrilateral is called a diagonal.

* The sum of two diagonals of a quadrilateral is less than it’s perimeter.

**Parallelogram:** The quadrilateral whose opposite sides are parallel is called a parallelogram.

## Properties of parallelogram:

- Opposite sides are equal and parallel to each other .
- Opposite angles are equal.
- Adjacent sides are unequal.
- Sum of adjacent of parallelogram 180
^{0}. - The diagonals of a parallelogram are not equal.
- The diagonals of a parallelogram bisect each other.

**Mensuration:**

- Formula of area of a parallelogram = Base × Height.
- Formula of perimeter of a parallelogram = 2(Length + breadth).

**Rectangle:** A rectangle is a parallelogram with one right angle.

Or, the parallelogram one of whose angle is a right is called a rectangle.

## Properties of a rectangle:

- Both pairs of opposite sides of a rectangle are equal.
- All the angles of a rectangle are equal and right angle.
- The diagonals of a rectangle are equal.
- The diagonals of a rectangle bisect each other.

## Mensuration:

- Area of a rectangle = Length × Breadth.
- Perimeter of a rectangle = 2(Length + breadth).
- Diagonal of a rectangle =

**Rhombus:** A rhombus is a parallelogram with equal sides.

Or, A rhombus is a parallelogram with two adjacent sides equal.

## Properties of rhombus:

- All the sides of a rhombus are equal.
- Both pairs of opposite angles of a rhombus are equal.
- None of the angles of a rhombus is a right angle.
- The diagonals of a rhombus are not equal.
- The diagonals of a rhombus bisect each other at right angle.
- Sum of adjacent of a rhombus 180
^{0}.

**Mensuration:**

- Area of a rhombus = ½×Product of length of diagonals.
- Perimeter of a rhombus = 4× Length of one side.

Square: A square is a rectangle that has two adjacent sides equal.

Or, a square is a rectangle with equal side.

## Properties of a square:

- All the sides of a square are equal.
- All the angles of a square are equal and right angle.
- The diagonals of a square are equal.
- The diagonals of a square bisect each other at right angle.

**Mensuration:**

- Area of a square = (Length of one side)
^{2} - Perimeter of a square = 4× Length of one side.
- Diagonal of a square: √2× Length of one side

**Trapezium:** The quadrilateral only two of whose side are parallel is called a trapezium.

* One of parallel sides of a trapezium is called the base and of the none parallel sides are called the lean sides or oblique sides.

* If two non non-parallel sides of a trapezium are equal, it is called an isosceles trapezium.

* The parallel sides of a trapezium cannot be equal.