Understanding Polygons – Class 8 : Notes
Plane Surface:
The flat surface that can be extended in all possible directions is called plane surface.
In other word- A two-dimensional flat surface extended indefinitely is called a plane surface.
Ex- Flat surfaces of cubes and cuboids, floors with zero thickness, etc.
Curve:
The figure traced out on a plane surface without lifting pencil is called curve.
Type of curve
- Open curve 2- Closed curve
Plane Curve:
It is a curve that lies in a single plane. It may be closed or open.
(a) Open curves: The curve that does not end at the starting point is called open curve.
(b) Closed curves: The curve that begins and ends at same point is called closed curve.
Polygon:
Any common closed curve composed of only line segments is called a polygon.
(i) Figures below show some curves that are polygons:
(ii) Figures below show some curves that are not polygons:
Classification of polygons:
The polygons can be classified into various types on the basis of their no of sides or vertices.
|
No of sides or vertices |
Name of polygon |
Figure of polygon |
|
3 |
Triangle |
|
|
4 |
Quadrilateral |
|
|
5 |
Pentagon |
|
|
6 |
Hexagon |
|
|
7 |
Heptagon |
|
|
8 |
Octagon |
|
|
9 |
Nonagon |
|
|
10 |
Decagon |
|
Interior and Exterior of a closed curve:
(a) Interior of a closed curve:
The area which is covered inside the closed curve is called its interior.
In the fig; the shaded portion reflects the interior of the given closed curve.
(b) Exterior of a closed curve:
The area which is covered outside the closed curve is called its exterior. In the fig; the shaded portion reflects the exterior of the given closed curve.
Type of Polygons
Convex and concave polygons:
(a) Convex polygons:
The polygon in which all diagonals lie inside the boundary of the polygon is called convex polygon.
For the given figure, all the diagonals (AD, AC, BE, BD, CE) formed are present in the interior of the polygon. And there are no diagonals possible outside the given polygon.
Note- Each angle of convex polygon is less than 1800.
(b) Concave polygons:
The polygon in which at least one diagonal lies outside the boundary of the polygon is called concave polygon.
For the given figure, the diagonal LN is present in the exterior of the polygon.
Regular and Irregular polygons:
1. Regular Polygon:
A polygon whose all sides and angles are equal (equilateral & equiangular) is called a regular polygon.
For example square, Equilateral triangle, etc.
In both square and triangle, the length of all the sides as well as the angles formed is equal.
2. Irregular Polygon:
A polygon whose all sides and angles are not equal is called an irregular polygon.
Ex- rectangle, kite, etc.
For the given rectangle figure, all the sides are not same. For the given triangle figure, neither the sides nor the angles are same.
(a) Angle sum property of triangle:
The sum of the three angles of a triangle is 180o.
(b) Sum of the measure of the Exterior Angles of a Polygon:
The sum on the measures of the external angles of any polygon is 360o.