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CBSE Assignments class 09 Mathematics

  Mathematics Assignments & Worksheets  For  Class IX Chapter-wise mathematics assignment for class 09. Important and useful extra questions strictly according to the CBSE syllabus and pattern with answer key CBSE Mathematics is a very good platform for the students and is contain the assignments for the students from 9 th  to 12 th  standard.  Here students can find very useful content which is very helpful to handle final examinations effectively.  For better understanding of the topic students should revise NCERT book with all examples and then start solving the chapter-wise assignments.  These assignments cover all the topics and are strictly according to the CBSE syllabus.  With the help of these assignments students can easily achieve the examination level and  can reach at the maximum height. Class 09 Mathematics    Assignment Case Study Based Questions Class IX 

Proof of Pythagoras Theorem and its Converse

PYTHGORAS THEOREM AND ITS CONVERSE
CLASS 10 CHAPTER 6  

Proof of Pythagoras theorem and its converse for class X, complete explanation of the Pythagoras theorem and its converse, Statement and proof of Pythagoras theorem class x, statement and proof of converse of Pythagoras theorem. 


PROOF OF PYTHAGORAS THEOREM 
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STATEMENT:- In a right angled triangle sum of square of two sides of a triangle is equal to the square of the third side.

Given:- In triangle ABC, B = 90o

To Prove :- AB2 + BC2 = AC2

Construction: Draw BD δΈ„ AC

Proof:- InADB and ABC
1 = 3
A = A
            By AA rule
ADB~△ABC
    AB x AB =AC x AD
                                  AB2 = AC x AD  ................(1)
           InBCD and ACB
2 = 3
C = C
          By AA rule
BCD~△ACB
     BC x BC =AC x CD
                                 BC2 = AC x CD  ..............(2)

             Adding equation (1) and (2)
                    AB+ BC2  = AC X AD + AC X CD

                                  AB+ BC2  = AC(AD+CD)

                                 AB+ BC2   = AC X AC

                                 AB+ BC2   =  AC2
Hence prove the required theorem
*********************************************

PROOF OF CONVERSE OF PYTHAGORAS THEOREM

https://dinesh51.blogspot.com

STATEMENT:-
If sum of squares of two sides of a triangle is equal to the square of the third side then the angle opposite to the larger side is right angle.

GIVEN :- In triangle ABC,  AB+ BC2   =  AC2

TO PROVE:-  B = 90o

CONSTRUCTION:- 
Draw another DEF such that  AB = DE,  BC = EF, and E = 90o

PROOF:- 
In DEF , E = 90o
Therefore by Pythagoras Theorem

                         DE+ EF2   =  DF2  

Putting AB = DE and BC = EF we get

                        AB+ BC2   =  DF2   ..........................(1)
                But  AB+ BC2   =  AC2  ..........................(2)Given

From (1) and (2) we get

                       AC2 = DF2
               Or     AC = DF

Now InABC and DEF

                     AB = DE   ..................(By construction)
                     BC = EF .....................(By construction)
                     AC = DF ......................(Proved )

By SSS rule

In ABC  DEF

                          B = E  ...............(By CPCT)
                  But E = 90o
                       B = 90o

Hence prove the required result

THANKS FOR WATCHING AND READING
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