what is polygon? what are the types of polygon? what is the test to check point is inside the polygon or outside the polygon?

 Polygon :  It is a closed circuit which is made up of many line segments . It is 2dimentional geometric figure. As per name poly means many , a  2D shape having three or more than 3 sides.

Types of Polygon

  1.Simple polygon : There is no sides which are intersecting each other.

 2 .Complex polygon : In Complex polygon lines intersect each other.

3.Convex polygon :  In the convex polygon the angle between the two sides                 always less than 180 degree(angle<180). line joining by any two points taken in polygon it must be inside the polygon.

4.Concave polygon :  If any  angle between the two sides of polygon is greater           than 180 degree(angle >180) known as concave polygon. portion of the line made                  up  of two points should be  outside the polygon. 

  There is a test to check whether a point is inside the polygon or outside the polygon.

Inside test : It tells whether the point is inside the polygon or outside the polygon.

Odd Even Test

If the no. of intersecting points is odd then the point lies inside the polygon. If the no. of intersecting points is even then the point lies outside the polygon.

First we take a point and check the no. of intersecting point in any one direction.

In this figure (I) no. of intersecting points=3 (odd) ,so point is inside the polygon.

In figure(II) no. of intersecting points=2(even) , so point is outside the polygon.

How to solve when two joining sides of polygon is intersect the line extended by the point?

In the figure(III) points A and B both are in same direction ,consider it as even. let 2 and 1 another intersecting point 2+1=3(odd) . point is inside the polygon.

In figure (IV) points A and B both are the opposite direction , consider it as odd . let 1 and another 1 intersecting point 1 so 1+1=2(even). point is outside the polygon.