POLYGONS

The word polygon means having many sides. Therefore a closed plane figure made up of several line segments that are joined together is called a polygon.

For example, a triangle, a quadrilateral are polygons.

NB. A circle is not a polygon as it is not made of line segments.

Diagonals: The number of diagonals in a polygon of sides n is n(n-3)/2



Types of polygons
   
Regular polygons:  A polygons having all angles and all sides are equal is called a regular polygon.

Irregular polygons:  A polygon may have unequal angles and sides. Such polygons are called irregular polygon.

Name of polygons according to their sides

Name                               Number of sides

Triangle                                        3

Quadrilateral                               4

Pentagon                                       5

Hexagon                                        6

Heptagon                                       7

Octagon                                          8

Nonagon                                         9

Decagon                                        10

Types of angle of a polygon

Interior Angle:  angle formed by two adjacent sides inside the polygon.

Sum of Interior Angles in a Regular Polygon of Sides n is: 

(n-2) × 180 degree

Exterior Angle:  angle formed by two adjacent sides outside the polygon.

Sum of Exterior Angles in a Regular Polygon of Sides n is: 

360 degree

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                          V Amar Ganit.pdf
               VI Ganit Prabha.pdf
             VII Ganit Prabha.pdf
             VIII Ganit Prabha.pdf
        IX Ganit Prakash.pdf







Prove that,   CosA + CosB + CosC + Cos(A + B + C) =  4 Cos(A + B)/2 Cos(B +C)/2 Cos(C+A)/2


Sol. 

  CosA + CosB + CosC + Cos(A + B + C)

=  2Cos(A+B)/2 Cos(A-B)/2   +2cos(C+A+B+C)/2 Cos(C-A-B-C)/2

= 2Cos(A+B)/2 Cos(A-B)/2   +2cos(A+B+2C)/2 Cos(-A-B)/2 

= 2Cos(A+B)/2 Cos(A-B)/2     +2cos(A+B+2C)/2 Cos(A+B)/2

= 2Cos(A+B)/2[Cos(A-B)/2       +Cos(A+B+2c)/2]

= 2Cos(A+B)/2[2Cos(2A+2C)/4               Cos(-2B-2C)/4]

= 2Cos(A+B)/2[2Cos(A+C)/2 Cos(B+C)/2]

= 4Cos(A+B)/2 Cos(B+C)/2 Cos(C+A)/2

Hence proved.

How to score good marks in Mathematics

1. Understand the basic principles and concepts.

2. Maintain a formula book.

3. Practice more and more.

4. Study in distraction free environment.

RRB NTPC Admit Card And Exam 2019


according to the CEN 01/2019 notification, RRB NTPC Exam will be held between June to Sept 2019 And ADMIT CARD Will be release soon.



    Candidates  would be able to download their RRB NTPC Hall Ticket 2019 through the official website of RRBs.

    CBT 1st Stage exam will be consists of one objective paper 100 questions from General Awareness (40Marks), Mathematics (30 Marks); and General Intelligence & reasoning (30 Marks).