Converse of Pythagoras Theorem

 

“               What is Pythagoras Theorem ?

 

As in the diagram, ABC is a right-angled triangle

with right angle at C, then

 

          a2 + b2 = c2

 

 


The converse of Pythagoras Theorem is:

 

If

              a2 + b2 = c2        holds

 

then

          DABC is a right angled triangle with

          right angle at C.

 

 

 

 


How to prove The converse of Pythagoras Theorem ?  

Now construct another triangle as follows :

 

      EF = BC = a

ÐF is a right angle.

   FD = CA = b

 

   In  DDEF,

   By Pythagoras Theorem,

          ……..(2)

   By (1), the given,

         

   Theorefore,                 AB = DE

   But by construction,       BC = EF

   and                                 CA = FD

                             D ABC @ D DEF (S.S.S.)

 

 

 

 


Lesson

 

We use Pythagoras Theorem and the concept of congruent triangles to prove the Converse of Pythagoras Theorem.