**What is a Quadrilateral**

A closed figure bounded by four line segments is called a quadrilateral.

All closed figures shown in figure are quadrilaterals as all of them have four line segments. A quadrilateral has four sides, four vertices, and four angles. Let us consider a quadrilateral PQRS.

- Sides of the quadrilateral PQRS are PQ, QR, RS, SP, or QP, PS, SR, RQ.
- Angles of the quadrilateral PQRS are ∠P, ∠Q, ∠R, ∠S or ∠SPQ, ∠PQR, ∠QRS, ∠RSP.
- Vertices of quadrilateral PQRS are P, Q, R, and S.

**Read More:**

- Quadrilateral Family
- Different Kinds of Quadrilateral
- More Solved examples on Quadrilaterals
- Convex and Concave Quadrilaterals
- RS Aggarwal Class 9 Solutions Quadrilaterals and Parallelograms
- Properties of Cyclic Quadrilaterals

In addition to the above mentioned features, a quadrilateral also has two diagonals. The line segments joining the opposite vertices of a quadrilateral are called its diagonals. So, PR and QS are diagonals of quadrilateral PQRS that divide the quadrilateral into four triangles.

**Adjacent sides**

In quadrilateral PQRS, the two sides PQ and QR having a common end point Q, are called adjacent sides. Similarly, QR and RS, RS and SP, SP and PQ are adjacent to each other.

**Opposite sides**

The sides PQ and RS, PS and QR are opposite to each other. They are the opposite sides.

They do not have any common point.

**Adjacent angles**

Two angles of a quadrilateral that have a common arm are called adjacent angles.

In quadrilateral PQRS

∠P and ∠S, ∠P and ∠Q, ∠Q and ∠R, ∠R and ∠S are pairs of adjacent angles.

**Opposite angles**

Two angles of a quadrilateral that have no common arm are called opposite angles.

In quadrilateral PQRS, ∠P and ∠R, and ∠Q and ∠S are pairs of opposite angles.

## Types of Quadrilaterals:

Quadrilaterals are classified as the following, depending upon their sides.

- Parallelogram
- Rhombus
- Rectangle
- Square
- Trapezium
- Isosceles Trapezium
- Kite

**Interior and exterior of a quadrilateral**

A quadrilateral divides a plane into three parts:

**Interior region:**The region inside the quadrilateral is called the interior of the quadrilateral.

Points A, B, and C are in the interior of the quadrilateral PQRS.**On the quadrilateral:**The points M and N which lie on the boundary are said to be on the quadrilateral.**Exterior region:**The region outside the quadrilateral is called the exterior of the quadrilateral. Points U and T are in the exterior of the quadrilaterals.

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