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 –
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpt-7o0MHGBEfj0_wrI54ZCUSSiP4-RycHKtmkxjlrSdee_kpJ6M6EH9PQ1btndw8wtt3MJuW3_6LUX_FiF_tvxQ1RenetnfzgyCUQ9R1PgD43EQFPe2S-gZgY-nEDdFExCkfVD4yRVDQ/w400-h339-rw/567567%2527.png)
- 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
- AB and BC,
- BC and CD,
- CD and DA,
- DA and AB
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLs6nwwRke2QDac-SO_kcZDq2zTyU1-xOdo6ixj_OQpmt68jXfmpAMlSee453Zhh3K5y5tGkzXeDT3ltpXZH7E8mBIBkDXBFlsOgZeZ92_jOOemb18LPpYSJivN0lDxVFwfF3gVv7cN50/w400-h266-rw/56.png)
- It refers to the endpoints of the same side of the polygon.
- As in the above figure
- A and B,
- B and C,
- C and D,
- D and A
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
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjO5BhNHGzzAAxUVDkaHfu-vhod9GdmkDn6jI7RTpoQDLSPNLPe8nMIa1vvHbtqhTGcPeQELfa5j9BlcmlMxSe3hY0Cf2poe2OkHQpKOxB-aQvm7lw4EfcO3KA45pDwZz9i9StL1MAtP_A/d-rw/687.png)
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
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgE_NhF53I8pgow1jPLOLEZ5ztrFjch0hixpe9gSJ7NFDp7mpWXutHGa8CkurBfkHSkNNVhBvDliGoXWkAW6dSV4UuKA3OTxMmQE9PMKNIK6yoYIKRV3bl0xt7mG96L0HotfQTDEFfcigU/s0-rw/1.png)
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.