IN THE FIGURE AB = AC. PROVE THAT BD = BC
 

Dear Student,

Please find below the solution to the asked query:

Given :  AB  =  AC , So from base angle theorem we get

ABC  =  ACB                                           --- ( 1 )

And
BD  =  BC , So from base angle theorem we get

BDC  =  BCD                                           --- ( 2 )  , ACB  =  BCD ( Same angles ) , So from equation 1 a nd w we get

ABC  =  ACB  = BDC                                     --- ( 3 )

From angle sum property in triangle we get in triangle ABC :


BAC +  ABC + ACB =  180° , Substitute values and get

40° + ABC  +   ABC = 180°

2 ABC = 140°

ABC =  70° , So From equation 3 we get

ABC  =  ACB  = BDC = 70°

And

CBD  = ABC - ABD  = 70° - 30°  =  40° 

And

ADB  = 180° - ABD - BAD  = 180° - 30° - 40°  =  110°                   

Hope this information will clear your doubts about Congruence of Triangles.

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Regards

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