in triangle ABC , AD is the bisector of such that AD is perpendicular to BC. Prove that triangle ABC is an isoceles triangle

Dear Student,

Please find below the solution to the asked query:

We form diagram from given information , As :

In ABD and    ACD 

BAD =   CAD                                        ( Given AD is angle bisector )

AD  = AD                                                       ( Common side )


BDA =   CDA = 90°                             ( Given AD is also perpendicular on BC )


ABD   ACD                                       ( By ASA rule ) 


  ABD  =  ACD                                      ( By CPCT )                   --- ( 1 )

We know from base angle theorem  ( As ABC  =  ACB  from equation 1 )  that AB  =  AC  , So

ABC is a isosceles triangle .                                                                   ( Hence proved )

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