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Polygons

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Polygons - Lesson Summary

Curve
A plane figure formed by joining a number of points without lifting a pencil from the paper and without retracing any portion  of the drawing other than single points is called a curve.

Open curve
A curve which does not cut itself is called an open curve.

Closed curve
A curve which cuts itself is called an open curve.

Simple closed curve
A closed curve is called a simple closed curve, if it does not pass through one point more than once.

Polygon:
A polygon is a simple closed figure made up of only line segments such that no two line segmrents intersect expect at their end points and no two line segmrents with a common end points are coincident.

We can classify polygons according to the number of sides or vertices.

The simple polygon is a triangle. A triangle has three sides  thus, it is a three-sided polygon.

A four-sided polygon is called a quadrilateral. A 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 polygon has an n-sided, it is called an n-gon.



Each side of a polygon is connected by two consecutive vertices of the polygon.
A diagonal is a line segment that connects the non-consecutive vertices of a polygon.

Adjacent sides
Any two sides with a common end point are called the adjacent sides of the polygon.

Adjacent vertices
The end ponts of the same side of a polygon are called the adjacent vertices.

Diagonals
The line segments obtained by joining vertices which are not adjacent are called the diagonals of a polygon.

Concave polygon:
If a diagonal lies outside a polygon, then the polygon is called a concave polygon.

Convex polygon:
If all the diagonals lie inside the polygon, then the polygon is said to be a convex polygon.

If there are n- sides of a convex polygons and n > 3, then it has n(n - 3) 2 diagonals.



Regular polygon:
A 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.

Irregular polygon:
The polygon with unequal sides and unequal angles is called an irregular polygon.



ANGLE SUM PROPERTY:
The sum of all interior angles of a polygon is called the angle sum.

Angle sum of a polygon = ( n - 2) x 180° , where n = number of sides of the polygon.

A regular polygon of n sides ( n ≥ 3) then its each interior angle is equal to 2n - 4 n right angles i.e 2n - 4 n ×90°.
           
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 360°.

Measure of each exterior angle of an n sided regular polygon is 360 ⁰ n .



Angle sum of a polygon = ( n - 2) x 180° .

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