## Polygons:

A polygon is a **closed curve (figure)** formed by the line segment such that:

1) No two line segments intersect except at their end-points.

2) No two line segments with a common end points are coincident.

The **line segments forming a polygon** are called its **sides** and the **end-points of the line segments** are called its **vertices**. In other words, the **meeting point of a pair of sides is called a vertex of the polygon**.

ABC is a polygon having three sides AB, BC and CA. Points A, B, C are known as the vertices. As the figure consists of three sides. So, it is called a triangle.

is a polygon with four sides AB, BC, CD and DA. It has four vertices A, B, C and D. Such a figure is called a quadrilateral. Line segments AC and BD are known as diagonals.

A closed figure formed by five line segments is known as a pentagon.

is a pentagon with AB, BC, CD, DE and EA as five sides. A, B, C, D and E are five vertices of the pentagon. Line segments AC, AD, BD and BE are diagonals.

is not a polygon as BC is not a line segment.

## Adjacent Sides:

**Any two sides with a common end-point (vertex)** are called the adjacent sides of the polygon.

## Adjacent Vertices:

The **endpoints of the same side of a polygon** are known as the adjacent vertices.

## Diagonals:

The **line segments obtained by joining vertices which are not adjacent** are called the diagonals of the polygon.

## Convex Polygon:

A polygon is a convex polygon if the **line segment joining any two points inside it lies completely inside the polygon**.

the line segment joining P and Q does not line completely inside the polygon ABCDE. So, it is not a convex polygon.