Solve 23rd sum,h having doubt

Dear Student,

Please find below the solution to the asked query:

Given : AB  =  AC , From base angle theorem we get 

$\angle$ ABC  =  $\angle$ ACB  =  x                                --- ( 1 )

And we know from external angle theorem :

$\angle$ CAD  =  $\angle$ ABC  +  $\angle$ ACB , Substitute values from equation 1 we get

$\angle$ CAD  =  x +  x ,

$\angle$ CAD  = 2 x  , Also given AE is bisector of $\angle$ CAD , So

$\angle$ DAE  = $\angle$ CAE  =  x                                --- ( 2 )

From equation 1 and 2 we get

$\angle$ DAE =  $\angle$ ABC  and these are corresponding angles , we take BD as transversal line and that can only be true if

BC  | | AE                                                         ( Hence proved )


Regards