Question

Can somebody provide me with the proof of converse of Pythagoras theorem? Its really urgent

Answer 1

CONVERSE OF PYTHAGORAS THEOREM
STATEMENT : - In   a   △ ,   if   the   sum   of   the   squares   of   2   sides   is   equal   to   square   of   third   side ,   then   angle   opposite   to   third   side   is   right   angle GIVEN : -



ABC   is   a   △   in   which   AC2  =   AB2   +   BC2
To   Prove : -       ∠ B   =   90 °
Construction : -       Draw   a   △   PQR   right   angled   at   Q ,   such   that                                      
 QR   =   BC   and   PQ   =   AB


Proof : - In   △   ABC , AC2 =   AB2 +   BC2    [ given]     . . . . . . . . . . 1
Now ,   PQ   =   AB    [ By   construction]
QR   =   BC ∴   From   1 ,  
AC2   =   PQ2   +   QR2     . . . . . . . . . . 2
Now ,   from   △   PQR ,
PR2   =   PQ2   +   QR2       [Pythagoras   theorem ]
∴   from   2 ,   we   get ,          
AC2   =   PR2
⇒   AC   =   PR
Now ,   In   △   ABC   and   △   PQR ,
AB   =   PQ     [By   construction]
BC   =   QR     [By   construction]
AC   =   PR     [Proved   above]
⇒   ABC   ≅   △   PQR     [SSS]
⇒   ∠   B   =   ∠   Q    [ c   p   c   t ]
⇒   ∠   B   =   90 °

 

Answer 2

here is the answer
hope it helps