Polygons

Polygon

A closed plane figure bounded by three or more line segments is called a polygon.

The line segments forming the polygon are called its sides.
The point of intersection of sides are called its vertices. The number of vertices is equal to the number of sides.

    A polygon with
  • 3 sides is called a triangle.
  • 4 sides is called a square.
  • 5 sides is called a pentagon.
  • 6 sides is called a hexagon.
  • 7 sides is called a heptagon.
  • 8 sides is called a octagon.
  • 9 sides is called a nonagon.
  • 10 sides is called a decagon.

Convex Polygon

A polygon each of whose interior angles is less than 180° is called a convex polygon. When the angles are greater than 180° it is known as concave polygon.

Diagonals of a polygon

A line segment joining any two non-consecutive vertices of a polygon is called a diagonal.

Sum of interior angles

Sum of interior angles of a polygon of n sides = (2n - 4)right angles.

Sum of exterior angles

Sum of all exterior angles of a polygon is 360°.

Regular Polygon

A polygon with all sides equal and all interior angles equal is called a regular polygon.
    A regular polygon has
  • Each interior angle = [(2n-4)×90/n]°
  • Each exterior angle = (360/n)°
  • n = 360/(each exterior angle)
  • Exterior angle = 180° - interior angle.



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