**What is a Quadrilateral? **Quadrilateral is a four sided polygon. It is a closed figure bounded by four sides. **Example:** Floor of a room, walls of a room, ceiling of a room, computer screen, The surface of a note book.

### Types of Quadrilaterals:

The quadrilaterals are classified into different names according to the relationship of their sides and the angles.

The different types of Quadrilaterals are,
Parallelogram, rhombus, rectangle, square, trapezoid, concave and convex
quadrilaterals.

**1. ****Parallelogram:** It is a quadrilateral whose pair of opposite sides are parallel.

**2. Rhombus: **It is a parallelogram whose sides are of congruent.

**3. ****Rectangle:** It is a parallelogram whose interior angles measure 90

^{o} .

**4. ****Square:** It is a parallelogram whose sides are congruent and the interior angles measure 90

^{o} .

**5. ****Trapezoid:** It is a quadrilateral whose one pair of opposite sides are parallel.

**6. ****Kite:** It is a quadrilateral which has two distinct pairs of adjacent sides are congruent.

**Regular Quadrilateral:** Regular Quadrilaterals are those in which the sides are of equal length and interior angles are equal. Square is a regular quadrilateral whose sides are of equal measure and the interior angles measure 90

^{o} .

**Irregular Quadrilateral:**
The quadrilaterals which are not regular, are called irregular
quadrilaterals. In an irregular quadrilateral, all sides are not equal
and the interior angles are not of same measure.

**Concave Quadrilateral:** Concave quadrilaterals, are those in which one of its interior angle measure more than 180

^{o} (reflex angle). The above diagram shows a concave quadrilateral.

**Convex Quadrilateral:** A quadrilateral whose interior angles measure less than 180

^{0} ( acute or obtuse ) is called a convex quadrilateral.

Square, Rectangle, Parallelogram, Rhombus, Trapezoid are all convex quadrilateral.

**Properties of Quadrilaterals:**

1.

**Properties of a Parallelograms:**a. Opposite sides are parallel.

b. Opposite sides are congruent.

c. Opposite angles are congruent.

d. Pair of consecutive angles are supplementary.

e. Diagonals bisect each other.

2.

**Properties of a Rhombus:**a. Opposite sides are parallel.

b. All the four sides congruent.

c. Opposite angles are congruent.

d. Pair of consecutive angles are supplementary.

e. Diagonals bisect each other.

3.

**Properties of a Rectangle:**a. Opposite sides are parallel.

b. Opposite sides are congruent.

c. Each of interior angle measure 90

^{o} .

d. Diagonals are congruent.

e. Diagonals bisect each other.

4.

**Properties of a Square:**a. Opposite sides are parallel.

b. All the four sides are congruent.

c. Each of interior angle measure 90

^{o}.

d. Diagonals are congruent.

e. Diagonals bisect each other.

5.

**Properties of a Trapezoid:**a. It has one pair of opposite sides parallel.

b. The interior angles on the same side of the non-parallel lines are supplementary.

6.

**Properties of Isosceles Trapezoid:** a. It has one pair of opposite sides parallel.

b. The non parallel sides are congruent.

c. The lower base angles are congruent.

d. The upper base angles are congruent.

e. Diagonals are congruent.

f. Pair of a lower base angle and an upper base angle is supplementary.

**Similar Quadrilaterals:** The pair of quadrilaterals are said to be similar if their corresponding interior angles are equal and the corresponding sides are proportional. The following diagram shows pairs of quadrilaterals which are similar.

**Cyclic Quadrilaterals:** Quadrilaterals whose vertices lie on the circumference of a circle are called cyclic quadrilaterals.

The following diagram shows the cyclic quadrilaterals.

**The Properties of Cyclic Quadrilaterals:**1. Opposite angles of a cyclic quadrilateral is equal to 180

^{o} .

2. Exterior angles of a cyclic Quadrilateral is equal to the interior opposite angle.