# What is a Quadrilateral? | Definition, Types and Properties

The quadrilateral is a figure formed by adding the four-line segments. It consists of 4 sides, 4 vertices, and two diagonals. By going through this entire article you will get a complete idea of Quadrilateral like Types, Sides, Angles, Vertices, Diagonals of it, its Properties etc. If P, Q, R, S are four points and where no three points are collinear and also the line segments PQ, QR, RS, and SP do not intersect at their endpoints. Check the below figure that is the quadrilateral PQRS. In a quadrilateral PQRS
(i) The vertices in a quadrilateral are P, Q, R, S.
(ii) The sides of a quadrilateral are PQ, QR, RS, and SP.
(iii) Also, the angles of quadrilateral are ∠SPQ, ∠PQR, ∠QRS and ∠RSP.
(iv) The line segments are PQ and QS.

## Convex Quadrilaterals and Concave Quadrilaterals

If each angle of a quadrilateral is less than 180°, then it is called a convex quadrilateral. Also, if one angle of the quadrilateral is more than 180°, then it is called a concave quadrilateral. A quadrilateral is not a simple closed figure.

### Sides, Angles, Vertices, Diagonals of the Quadrilateral

Have a look at the complete details of a Quadrilateral below.

#### Adjacent Sides of a Quadrilateral

Adjacent Sides of a Quadrilateral are nothing but the sides that have a common endpoint. If PQRS is a Quadrilateral, then (PQ, QR), (QR, RS), (RS, SP), and (SP, PQ) are four pairs of adjacent sides of quadrilateral PQRS.

#### Opposite Sides of a Quadrilateral

In a given quadrilateral, the two sides are said to be opposite sides when they do not have a common endpoint. If PQRS is a quadrilateral, then (PQ, SR) and (PS, QR) are two pairs of opposite sides of quadrilateral PQRS.

#### Adjacent Angles of a Quadrilateral

An angle is formed when two rays meeting at a common endpoint. Two angles of a quadrilateral are said to be adjacent when they have a common arm. From the given figure, (∠P, ∠Q), (∠Q, ∠R), (∠R, ∠S), and (∠S, ∠P) are four pairs of adjacent angles of quadrilateral PQRS.

#### Opposite Angles of a Quadrilateral

Opposite Angles of a Quadrilateral are not adjacent angles. If you consider a quadrilateral PQRS, then (∠P, ∠R) and (∠Q, ∠S) are two pairs of opposite angles of quadrilateral PQRS.

#### Adjacent Vertices of a Quadrilateral

In a Quadrilateral, if two vertices have a common side are known as adjacent vertices. From the figure, the pairs of adjacent vertices are (P, Q); (Q, R); (R, S), and (S, P).

#### Opposite Vertices of a Quadrilateral

Opposite Vertices of a Quadrilateral are vertices that do not have a common side. From the figure, the pairs of opposite vertices are (P, R) and (Q, S).

#### Diagonal of a Quadrilateral

When a line segment of the opposite vertices of a quadrilateral is joined, then the diagonal of the quadrilateral is formed. From the given figure, the two diagonals are PR and QS.

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