Main Parts of a Polygon

 What are Polygons? 

  • It is a 2d closed shape made of line segments / straight lines only. 

Different Parts of a Polygon 

Consider a Rectangle ABCD
Sides –

  • It refers to the line segments which form the polygon.
  • In the above figure AB, BC, CD, DA are its sides. 

Vertex –

  • Point where 2 line segments meet is a vertex .
  • In the above figure A, B, C and D are its vertices.

Adjacent Sides – 

  • If any 2 sides share a common endpoint they are said to be adjacent to each other thus called adjacent sides
  • In the above figure 
  1. AB and BC, 
  2. BC and CD, 
  3. CD and DA, 
  4. DA and AB 
       are adjacent sides. 
Adjacent Vertices – 
  • It refers to the endpoints of the same side of the polygon. 
  • As in the above figure
  1. A and B, 
  2. B and C, 
  3. C and D, 
  4. D and A 
     are adjacent vertices.

Diagonals –

  •  It refers to the joins of the vertices which are not adjacent to each other. 
  • In the above figure, AC and BD are diagonals of the polygon. 
 

Angles

  • A figure formed from 2 rays which share a common endpoint is called Angle. 
  • The rays forming the angle are known as its arms or sides. 
  • The common endpoint is known as its vertex.

An angle is also associated with 3 parts


1. Interior - 
  • It refers to the inside/inner area.
  • Point P lies in interior of the angle

2. Angle/boundary -

  •  It refers to the arms of the angle.
  • Point B lies on the angle

3. Exterior - 

  • It refers to the outside / outer area. 
  • Point R and Q lies in exterior of the angle 


Naming an Angle

  • While naming an angle the letter depicting the vertex appears in the middle. 
  • An angle can also be named just by its vertex.

Example

The above angle can also be named as ∠BOA or ∠AOB or ∠B

Triangle

It is a 3 sided polygon. It is also the polygon with the least number of the sides.

Vertices: A, B and C

Sides: AB, BC and CA

Angles: ∠A, ∠B and ∠C

Here, the light blue coloured area is the interior of the angle.

The black line is the boundary.

Whereas, the dark blue area is the exterior of the angle. 

Quadrilaterals 

It is a 4 sided polygon

Vertices: A, B, C, D

Sides: AB, BC, CD, DA

Angle: ∠A, ∠B, ∠C, ∠D

Opposite Sides: AB and DC, BC and AD

Opposite Angles: ∠B and ∠D, ∠A and ∠C

Adjacent Angles: ∠A and ∠B, ∠B and ∠C, ∠C and ∠D, ∠D and ∠A.