28 January 2014

Polygons & Its Classification : Maths

Polygons & Its Classification : Maths NCERT / CBSE Notes

We know a polygon is a simple closed figure made up of only line segments.  We can classify polygons according to the number of sides or vertices.
  • The simple polygon we know is a triangle. A triangle has three sides and, thus, is a three-sided polygon
  • four-sided polygon is called a quadrilateral.  
  • five sided polygon is called a pentagon.
  • In this manner, we can obtain a six-sided polygon called a hexagon, a seven-sided polygon, called a heptagon, and so on.
  • If we have an n-sided polygon, it is called an n-gon.
Classification of Polygon
Polygons & Its Classification : Maths, CBSE / NCERT Revision notes
  • We know that each side of a polygon is connected by two consecutive vertices of the polygon.
  • diagonal is a line segment that connects the non-consecutive vertices of a polygon.  
  • If a diagonal lies outside a polygon, then the polygon is called a concave polygon.
  • If all the diagonals lie inside the polygon, then the polygon is said to be a convex polygon.
  • regular polygon is equiangular and equilateral. The word equiangular means, the interior angles of the polygon are equal to one another. The word equilateral means, the lengths of the sides are equal to one another.
  • The polygon with unequal sides and unequal angles is called an irregular polygon.

The sum of all interior angles of a polygon is called the angle sum.
At one vertex, we extend a side. This side makes an angle with its consecutive side. This angle is called the exterior angle. The interior angle and the exterior angles are adjacent angles.  These angles form a linear pair. Hence the sum of the exterior angles of any polygon is 
sum of all interior angles, angle sum, exterior angle, adjacent angles, sum of the exterior angles

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