Answer :

WE HAVE TO PROVE

In Δ ABC ray AD is an angle bisector.


Draw an parallel line to AD from C and extend the BA name the meeting point as E.


Now, AD to CE



If CB is a transversal to parallel line AD & CE


Then, BAD ≡ AEC (by Converse alternate angle test)


If AC is a transversal to parallel line AD & CE


CAD ≡ ACE


AD is an angle bisector


CAD ≡ BAD


Now, in Δ AEC


From 1 & 2 relations we can say that


CAD ≡ ACE


If base angles are congruent then segment AC ≡ segment AE


In Δ EBC,


Segment AD segment CE


AC = AE



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