We will learn about polygon and its classification.

A paper represents a plane surface. When we doodle with a
pencil on it without lifting out or without using a ruler, some drawings are
made which are called **curves**.

Curves which begin and end at the same point are called **closed curves**.

Curves which begin and end at the same point but do not
cross themselves are called **simple
closed curves**.

Curves which begin and end at different points are called **open curves**.

Definition of Polygon:

A polygon is a simple closed curve made up of straight line segments only.

The adjoining figure is a polygon.

(i) closed

(ii) bounded by five line segments AB, BC, CD, DE and AE.

Also, it is clear from the given polygon that:

(i) the five line segments AB, BC, CD, DE and AE intersect at their end points.

(ii) two line segments, with a common vertex, are not collinear i.e. the angle at any vertex is not 180°.

Parts
of a polygon:

(i) Line segments forming a polygon are called **sides of the polygon**.

(ii) The point where two sides of a polygon meet is called
the **vertex of the polygon**.

(iii) The line segment containing two non-adjacent vertices
is called the **diagonal of the polygon**.

(iv) The angle formed at the vertices inside the closed figure are called interior angles.

**Note:** The number of sides in a polygon is equal to
the number of vertices.

Classification of polygons:

Polygons are classified according to the number of sides or vertices they have.

Diagonal of a polygon:

A line segment connecting any two non-consecutive vertices is called the diagonal of a polygon.

**Some examples showing the diagonal of different polygons:**

The **formula for
finding the number of diagonals of **a polygon is [n(n - 3)]/2, where 'n' is
the number of sides.

**Note:** The polygon triangle has no diagonals.

**Some examples showing
the sides, vertices and diagonals of different polygons:**

In the adjoining figure AB, BC and CA are the three sides; A, B and C are the three vertices and there is no diagonal. |

In the adjoining figure AB, BC, CD and DA are the four sides; A, B, C and D are the four vertices and AC and BD are the two diagonals. |

In the adjoining figure AB, BC, CD, DE and EA are the five sides; A, B, C, D and E are the five vertices and AC, BD, EB, DA, and CE are the five diagonals. |

**● **Polygons

Polygon and its Classification

Interior and Exterior of the Polygon

Number of Triangles Contained in a Polygon

Angle Sum Property of a Polygon

Problems on Angle Sum Property of a Polygon

Sum of the Interior Angles of a Polygon

Sum of the Exterior Angles of a Polygon

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