ABC and DBC are two isosceles triangles on the same base BC. Show
that 

The correct answer is: Hence proved

Aim :- Prove ∠ ABD = ∠ ACD
Explanation :-
In triangle ABC, AB = AC (isosceles triangle )
so, ∠ ABC = ∠ ACB
In triangle BDC, BD = DC (isosceles triangle )
∠ DBC =∠ DCB
Adding above results we get,
∠ABC  + ∠ DBC = ∠ ACB + ∠ DCB
[ from diagram we get ∠ ABC  + ∠ DBC = ∠ ABD and ∠ ACB + ∠ DCB = ACD
 ∠ ABD = ∠ACD
Hence proved